{"id":32,"date":"2016-10-03T18:03:26","date_gmt":"2016-10-03T18:03:26","guid":{"rendered":"http:\/\/mitmgmtfaculty.mit.edu\/rfreund\/research-publications\/"},"modified":"2025-09-03T18:50:46","modified_gmt":"2025-09-03T18:50:46","slug":"research-activities","status":"publish","type":"page","link":"https:\/\/mitmgmtfaculty.mit.edu\/rfreund\/research-activities\/","title":{"rendered":"Pubs\/Talks\/Collaborators"},"content":{"rendered":"
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I support and stand with people who are not of my race \u2014 in the academic community and elsewhere \u2014 in protest against hate, brutality, divisiveness, fear, indifference, inequality, and discrimination.<\/h2>\n<\/blockquote>\n<\/div><\/div>

Publications<\/a><\/h3>\n

Recent Talks<\/a><\/h3>\n

Current and Former Students and Coauthors<\/a><\/h3>\n

\u00a0_<\/span><\/p>\n<\/div><\/div>

Publications<\/h2>

Books<\/h3>\n

Data, Models, and Decisions: The Fundamentals of Management Science<\/em><\/a>, with Dimitris Bertsimas, Southwestern College Publishing, 2000, republished by Dynamic Ideas LLC, 2004.<\/p>\n

<\/h3>\n

 <\/p>\n

Refereed Journal Articles<\/h3>\n

\u201cUsing Taylor-approximated Gradients to Improve the Frank-Wolfe Method for Empirical Risk Minimization<\/a>,\u201d with Zikai Xiong, SIAM Journal on Optimization<\/em> vol. 34 (3), pp. 2503\u20142534 (2024). [Working Paper<\/a>]\u00a0 [Additional Results and Extensions<\/a>]<\/p>\n

\u201cAnalysis of the Frank-Wolfe Method for Convex Composite Optimization involving a Logarithmically-Homogeneous Barrier<\/a>,\u201d with Renbo Zhao, Mathematical Programming <\/em>(2023) vol. 19, pp:123\u2013163. [Full Paper<\/a>]<\/p>\n

\u201cAn \u2018Oblivious\u2019 Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities<\/a>,<\/span>\u201d with Jourdain Lamperski and Michael Todd, Mathematics of Operations Research<\/i> vol. 49 (1), pp. 204-231 (2024) [Working Paper<\/a>]<\/p>\n

Generalized Stochastic Frank-Wolfe Algorithm with Stochastic \u2018Substitute\u2019 Gradient for Structured Convex Optimization<\/a>,\u201d with Haihao Lu, Mathematical Programming<\/em> vol. 187, pp. 317-349, 2021. [Working Paper<\/a>]<\/p>\n

\u201cAccelerated Residual Methods for the Iterative Solution of Systems of Equations<\/a>,\u201d with N. C. Nguyen, P. Fernandez, and J. Peraire, SIAM Journal on Scientific Computing<\/em> vol. 40 (5), pp. A3157-A3179, 2018. [Working Paper<\/a>]<\/p>\n

\u201cRelatively Smooth Convex Optimization by First-Order Methods, and Applications<\/a>,\u201d with Haihao Lu and Yurii Nesterov, SIAM Journal on Optimization<\/em> vol. 28 (1), pp. 333-354, 2018. [Working Paper<\/a>]<\/p>\n

\u201cNew Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure<\/a>,\u201d with Haihao Lu, Mathematical Programming<\/em> 170, pp. 445-477, 2018.<\/p>\n

\u201cAn Extended Frank-Wolfe Method with \u201cIn-Face\u201d Directions, and its Application to Low-Rank Matrix Completion<\/a>,\u201d with Paul Grigas and Rahul Mazumder, SIAM Journal on Optimization<\/em> 27(1), pp. 319-346, 2017. [Working Paper<\/a>]<\/p>\n

\u201cA New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives<\/a>,\u201d with Paul Grigas and Rahul Mazumder, Annals of Statistics<\/em> 45(6), pp. 2328-2364, 2017. [Working Paper<\/a>]<\/p>\n

\u201cFunctional regression for state prediction using linear PDE models and observations<\/a>,\u201d with N. C. Nguyen, H. Men, and J. Peraire, SIAM Journal on Scientific Computing<\/em> 38 (2), pp. B247-B271, 2016. [Working Paper<\/a>]<\/p>\n

\u201cNew Analysis and Results for the Frank-Wolfe Method<\/a>,\u201d (formerly titled \u201cNew Analysis and Results for the Conditional Gradient Method\u201d) with Paul Grigas, Mathematical Programming<\/em> 155 (1), pp. 199-230, 2016. [Working Paper<\/a>]<\/p>\n

\"Gaussian Functional Regression for Linear Partial Differential Equations<\/a>,\" with Nguyen, Ngoc C., Han Men, Robert M. Freund and Jaime Peraire, Computer Methods in Applied Mathematics and Engineering<\/em> Vol. 287, No. 15: 69-89, 2015.<\/p>\n

\u201cRobust topology optimization of three-dimensional photonic-crystal band-gap structures<\/a>,\u201d with H. Men, K. Y. K. Lee, J. Peraire, and S. G. Johnson, Optics Express<\/em> 22 (19), pp. 22632-22648, September 2014. [Working Paper<\/a>]<\/p>\n

\u201cFabrication-Adaptive Optimization, with an Application to Photonic Crystal Design<\/a>,\u201d with Han Men, Jaime Peraire, N.Cuong Nguyen, and Joel Saa-Seoane, Operations Research<\/em> 62 (2), pp. 418-434, 2014. [Working Paper<\/a>]<\/p>\n

\u201cAn Accelerated First-Order Method for Solving Unconstrained SOS Polynomial Optimization Problems<\/a>,\" with Dimitris Bertsimas and Xu Andy Sun, Optimization Methods and Software<\/em> 28 (3), pp. 424-441, 2013. [Working Paper<\/a>]<\/p>\n

\"Binary Optimization Techniques for Linear PDE-Governed Material Design<\/a>,\" with Saa-Seoane, Joel, Ngoc Cuong Nguyen, Han Men, Robert M. Freund, and Jaime Peraire, Journal of Applied Physics<\/em> A Vol. 109, No. 4: 1023-1030, 2012. [Working Paper<\/a>]<\/p>\n

\u201cDesign of Photonic Crystals with Multiple and Combined Band Gaps<\/a>,\u201d with H. Men, N.C. Nguyen, K.M. Lim, P. Parrilo, and J. Peraire, Physical Review<\/em> E 83 (4), 2011. [Working Paper<\/a>]<\/p>\n

\u201cBand Gap Optimization of Two-Dimensional Photonic Crystals Using Semi-definite Programming and Subspace Methods<\/a>,\" with H. Men, N.C. Nguyen, P. Parrilo, and J. Peraire, Journal of Computational Physics<\/em> 229 (10), pp. 3706-3725, 2010. [Working Paper<\/a>]<\/p>\n

\u201cEquivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model<\/a>,\u201d with Jorge Vera, Mathematics of Operations Research<\/em> 34 (4), pp. 869-879, 2009. [Working Paper<\/a>]<\/p>\n

\u201cAn Efficient Re-Scaled Perceptron Algorithm for Conic Systems<\/a>,\u201d with Alexandre Belloni and Santosh Vempala, Mathematics of Operations Research<\/em> 34 (3), pp. 621-641, 2009. [Working Paper<\/a>]<\/p>\n

\u201cOn the Second-Order Feasibility Cone: Primal-Dual Representation and Efficient Projection<\/a>,\u201d with Alexandre Belloni, SIAM Journal on Optimization<\/em> 19 (3), pp. 1073-1092, 2008. [Working Paper<\/a>]<\/p>\n

\u201cOptimizing Product Line Designs: Efficient Methods and Comparisons<\/a>,\u201d with Alexandre Belloni, Matthew Selove, and Duncan Simester, Management Science<\/em> (54) 9, pp. 1544-1552, 2008. [Working Paper<\/a>]<\/p>\n

\u201cA Geometric Analysis of Renegar\u2019s Condition Number, and its Interplay with Conic Curvature<\/a>,\u201d with Alexandre Belloni, Mathematical Programming<\/em> 119 (1), pp. 95-107, 2009. [Working Paper<\/a>]<\/p>\n

\u201cProjective Re-Normalization for Improving the Behavior of a Homogeneous Conic Linear System<\/a>,\u201d with Alexandre Belloni, Mathematical Programming<\/em> 118, pp. 279-299, 2009. [Working Paper<\/a>]<\/p>\n

\u201cBehavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems<\/a>,\u201d with Fernando Ord\u00f3\u00f1ez and Kim Chuan Toh, Mathematical Programming<\/em> 109 (vol. 2-3), pp. 445-475, 2007. [Working Paper<\/a>]<\/p>\n

\u201cOn the Symmetry Function of a Convex Set<\/a>,\u201d with Alexandre Belloni, Mathematical Programming<\/em> (111), pp. 57-93 , 2008. [Working Paper<\/a>]<\/p>\n

\u201cOn the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization<\/a>,\u201d Mathematical Programming<\/em> (106), pp. 527-545, 2006. [Working Paper<\/a>]<\/p>\n

\u201cOn Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems<\/a>,\u201d with Zhi Cai, Computational Optimization and Applications<\/em> (34) 3, pp. 299-320, 2006. [Working Paper<\/a>]<\/p>\n

\u201cOn an Extension of Condition Number Theory to Non-conic Convex Optimization<\/a>,\u201d with Fernando Ord\u00f3\u00f1ez, Mathematics of Operations Research<\/em> 30 (1), pp. 173-194, 2005. [Working Paper<\/a>]<\/p>\n

\u201cComputation of Minimum Volume Covering Ellipsoids<\/a>,\u201d with Peng Sun, Operations Research<\/em> 52 (5), pp. 690-706, 2004. [Working Paper<\/a>]<\/p>\n

\u201cComplexity of Convex Optimization using Geometry-Based Measures and a Reference Point<\/a>,\u201d Mathematical Programming<\/em> (99), pp. 197-221, 2004. [Working Paper<\/a>]<\/p>\n

\u201cOn the Complexity of Computing Estimates of Condition Measures of a Conic Linear System<\/a>,\u201d with Jorge Vera, Mathematics of Operations Research<\/em> 28 (4), pp. 625-648, 2003.<\/p>\n

\u201cComputational Experience and the Explanatory Value of Condition Numbers for Linear Optimization<\/a>,\u201d with Fernando Ord\u00f3\u00f1ez, SIAM Journal on Optimization<\/em> 14 (2), pp. 307-333, 2004. [Working Paper<\/a>]<\/p>\n

\u201cSolution Methodologies for the Smallest Enclosing Circle Problem<\/a>,\u201d with Sheng Xu and Jie Sun, Computational Optimization and Applications<\/em> 25, pp. 283-292, 2003.<\/p>\n

\u201cOn the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization<\/a>,\u201d SIAM Journal on Optimization<\/em> 13 (4), pp. 1004-1013, 2003. [Working Paper<\/a>]<\/p>\n

\u201cA New Condition Measure, Preconditioners, and Relations Between Different Measures of Conditioning for Conic Linear Systems<\/a>,\u201d with Marina Epelman, SIAM Journal on Optimization<\/em> 12 (3), pp. 627-655, 2002. [Working Paper<\/a>]<\/p>\n

\u201cCondition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definite Program<\/a>,\" with Manuel Nunez, SIAM Journal on Optimization<\/em> 11 (3), pp. 818-836, 2001. [Working Paper<\/a>]<\/p>\n

\u201cCondition Number Complexity of an Elementary Algorithm for Computing a Reliable Solution of a Conic Linear System<\/a>,\u201d with Marina Epelman, Mathematical Programming<\/em> 88 (3), pp. 451-485, 2000. [Working Paper<\/a>]<\/p>\n

\u201cInterior Point Methods: Current Status and Future Directions<\/a>,\u201d with Shinji Mizuno, in High Performance Optimization, H. Frenk et al. (eds.), Kluwer Academic Publishers<\/em>, pp. 441-466, 2000. [Working Paper<\/a>]<\/p>\n

\u201cCondition Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm<\/a>,\u201d with Jorge R. Vera, SIAM Journal on Optimization<\/em> 10 (1), 155-176, 2000. [Working Paper<\/a>]<\/p>\n

\u201cSome Characterizations and Properties of the \u2018Distance to Ill-Posedness\u2019 and the Condition Measure of a Conic Linear Systems<\/a>,\u201d with Jorge. R. Vera, Mathematical Programming<\/em> 86, pp. 225-260, 1999. [Working Paper<\/a>]<\/p>\n

\u201cCondition Measures and Properties of the Central Trajectory of a Linear Program<\/a>,\u201d with Manuel A. Nunez, Mathematical Programming<\/em> 83 (1), pp. 1-28, 1998. [Working Paper<\/a>]<\/p>\n

\u201cAn Infeasible-Start Algorithm for Linear Programming whose Complexity Depends on the Distance from the Starting Point to the Optimal Solution<\/a>,\u201d Annals of Operations Research<\/em> 62, pp. 29-58, 1996.<\/p>\n

\u201cFollowing a \u201cBalanced\u201d Trajectory from an Infeasible Point to an Optimal Linear Programming Solution with a Polynomial-time Algorithm<\/a>,\u201d Mathematics of Operations Research<\/em> 21 (4) 839-859, 1996.<\/p>\n

\u201cBarrier Functions and Interior-Point Algorithms for Linear Programming with Zero, One-, or Two-Sided Bounds on the Variables<\/a>,\u201d with Michael J. Todd, Mathematics of Operations Research<\/em> (20) 2, 415-440, 1995.<\/p>\n

\u201cA Potential Reduction Algorithm with user-specified Phase I - Phase II Balance, for Solving a Linear Program from an Infeasible Warm Start<\/a>,\u201d SIAM Journal of Optimization<\/em> (5) 2, 247-268, 1995.<\/p>\n

\u201cPrior Reduced Fill-In in Solving Equations in Interior-Point Algorithms<\/a>,\u201d with John Birge and Robert Vanderbei, Operations Research Letters<\/em> (11), pp. 195-198, 1992.<\/p>\n

\u201cA Potential Function Reduction Algorithm for Solving a Linear Program Directly from an Infeasible \u201cWarm Start\u201d<\/a>,\u201d Mathematical Programming<\/em> (52), pp. 441-466, 1991.<\/p>\n

\u201cProjective Transformation for Interior-Point Algorithms, and a Superlinearly Convergent Algorithm for the W-Center Problem<\/a>,\u201d Mathematical Programming<\/em> 58, pp. 385-414, 1993. [Working Paper<\/a>]<\/p>\n

\u201cA Method for the Parametric Center Problem, with a Strictly Monotone Polynomial-Time Algorithm for Linear Programming<\/a>,\u201d with K. C. Tan, Mathematics of Operations Research<\/em> (16), pp. 775-801, 1991.<\/p>\n

\u201cTheoretical Efficiency of a Shifted Barrier Function Algorithm for Linear Programming<\/a>,\u201d Linear Algebra and its Applications<\/em> (152), pp. 19-41, 1991.<\/p>\n

\u201cPolynomial-Time Algorithms for Linear Programming based only on Primal Scaling and Projected Gradients of a Potential Function<\/a>,\u201d Mathematical Programming<\/em> (51), pp. 203-222, 1991.<\/p>\n

\u201cOptimal Investment in Product Flexible Manufacturing Capacity<\/a>,\u201dwith C. Fine, Management Science<\/em> (36), pp. 449-466, 1990. [Working Paper<\/a>]<\/p>\n

\u201cCombinatorial Analogs of Brouwer\u2019s Fixed Point Theorem on a Bounded Polyhedron<\/a>,\u201d Journal of Combinatorial Theory<\/em>, Series B (47), pp. 192-219, 1989.<\/p>\n

\u201cAn Analog of Karmarkar\u2019s Algorithm for Inequality Constrained Linear Programs, with a 'New' Class of Projective Transformations for Centering a Polytope<\/a>,\u201d Operations Research Letters<\/em> (7), pp. 9-14, 1988.<\/p>\n

\u201cDual Gauge Programs, with Applications to Quadratic Programming and the Minimum Norm Problem<\/a>,\u201d Mathematical Programming<\/em> (38), pp.47-68, 1987.<\/p>\n

\u201cCombinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube<\/a>,\u201d Mathematics of Operations Research<\/em> (11) , pp. 169-179, 1986.<\/p>\n

\u201cPostoptimal Analysis of a Linear Program under Simultaneous Changes in Matrix Coefficients<\/a>,\u201d Mathematical Programming Study<\/em> 24, pp. 1-13, 1985. [Working Paper<\/a>]<\/p>\n

\u201cOn the Complexity of Four Polyhedral Set Containment Problems<\/a>,\u201d with James B. Orlin, Mathematical Programming<\/em> (33), pp.133-145, 1985.<\/p>\n

\u201cVariable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology<\/a>,\u201d Mathematics of Operations Research<\/em> (9), pp. 498-509, 1984.<\/p>\n

\u201cVariable Dimension Complexes, Part I: Basic Theory<\/a>,\u201d Mathematics of Operations Research<\/em> (9), pp. 479-497, 1984.<\/p>\n

\u201cOptimal Scaling of Balls and Polyhedra<\/a>,\u201d with B.C. Eaves, Mathematical Programming<\/em> (23), pp. 138-147 , 1982.<\/p>\n

\u201cA Constructive Proof of Tucker\u2019s Combinatorial Lemma<\/a>,\u201d with M.J. Todd, Journal of Combinatorial Theory<\/em> (30), pp. 321-325, 1981.<\/p>\n

 <\/p>\n

Papers submitted for Publication or in Preparation<\/h3>\n

\u201cThe Role of Level-Set Geometry on the Performance of PDHG for Conic Linear Optimization<\/a>,\u201d\u00a0with Zikai Xiong, submitted.<\/p>\n

\u201cComputational Guarantees for Restarted PDHG for LP based on \u201cLimiting Error Ratios<\/a>\u201d and LP Sharpness,\u201d\u00a0with Zikai Xiong, submitted.<\/p>\n

\u201cNonlinear conjugate gradient methods: worst-case convergence rates via computer-assisted analyses<\/a>,\u201d with Shuvomoy Das Gupta, Xu Andy Sun, and Adrien Taylor, January 2023.<\/p>\n

 <\/p>\n

Papers in Refereed Conference Proceeding<\/h3>\n

\u201cStochastic Frank-Wolfe for Constrained Finite-Sum Minimization\u201d with Geoffrey N\u00e9giar, Gideon Dresdner, Alicia Yi-Ting Tsai, Laurent El Ghaoui, Francesco Locatello, and Fabian Pedregosa, International Conference on Machine Learning (ICML), June 2020. [Full Paper<\/a>]<\/p>\n

\u201cAccelerating Greedy Coordinate Descent Methods,\u201d International Conference on Machine Learning (ICML), Stockholm, Sweden, July 2018. [Full Paper<\/a>] [Supplementary Material<\/a>]<\/p>\n

\u201cDesigning Phononic Crystals with Convex Optimization<\/a>\u201d with Han Men, N.-C. Nguyen, Joel Saa-Seoane, and Jaime Peraire, ASME2013 International Mechanical Engineering Congress and Exposition, pp. V014T15A047, San Diego, November 2013.<\/p>\n

\u201cA First-Order View of Boosting Methods: Computational Complexity and Connections to Regularization\u201d with Paul Grigas and Rahul Mazumder, International Workshop on Advances in Regularization, Optimization, Kernel Methods and Support Vector Machines: Theory and Applications, Leuven, Belgium July 2013.<\/p>\n

\u201cA Binary Optimization Method for Linear Metamaterial Design Optimization,\u201d with J. Saa-Seoane, N.-C. Nguyen, H. Men, and J. Peraire, to appear in 3rd International Conference on Metamaterials, Photonic Crystals and Plasmonics<\/em>, 2012.<\/p>\n

\u201cAn Efficient Re-Scaled Perceptron Algorithm for Conic Systems<\/a>,\u201d with Alexandre Belloni and Santosh Vempala, Proceedings of the 2007 Conference on Learning Theory<\/em>. [Working Paper<\/a>]<\/p>\n

\u201cAn Improved Training Algorithm for Support Vector Machines<\/a>,\u201d with Edgar Osuna and Federico Girosi, in Proceedings of IEEE NNSP\u201997<\/em>, Amelia Island, Florida, September 1997. [Working Paper<\/a>]<\/p>\n

\u201cTraining Support Vector Machines: an Application to Face Detection<\/a>,\u201d with Edgar Osuna and Federico Girosi, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition<\/em>, Puerto Rico, June 1997. [Working Paper<\/a>]<\/p>\n

 <\/p>\n

Edited Volumes and Invited papers in Conference Proceedings<\/h3>\n

\u201cInterior Point Methods: Current Status and Future Directions<\/a>,\u201d with Shinji Mizuno, Optima 51, pp. 1-9, 1996. [Working Paper<\/a>]<\/p>\n

Guest Editor, special volume of Annals of Operations Research<\/em> on Interior Point Methods in Mathematical Programming, 1996.<\/p>\n

\u201cEconomic Analysis of Product Flexible Manufacturing System Investment Decisions,\u201dwith C. Fine, Proceedings of the Second ORSA\/TIMS Conference on Flexible Manufacturing Systems<\/em>, 1986, (invited, not refereed), Kathryn Stecke and Rajan Suri, (eds.), Elsevier, Amsterdam, 1986. [Working Paper<\/a>]<\/p>\n

 <\/p>\n

Others<\/h3>\n

\u201cOn the Relation Between LP Sharpness and Limiting Error Ratio and Complexity Implications for Restarted PDHG,\u201d with Zikai Xiong, MIT Operations Research Center working. [Working Paper<\/a>]<\/p>\n

\u201cCondition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods,\u201d with Paul Grigas and Rahul Mazumder, arXiv:1810.08727, 2018. [Working Paper<\/a>]<\/p>\n

\u201cAdaBoost and Forward Stagewise Regression are First-Order Convex Optimization Methods,\u201d with Paul Grigas and Rahul Mazumder, MIT Operations Research Center working paper OR 397-14, 2014. [Working Paper<\/a>]<\/p>\n

\u201cBandwidth optimization of single-polarization single-mode photonic crystal fibers,\u201d with Han Men, Jaime Peraire, and N.Cuong Nguyen, 2013.<\/p>\n

\u201cCondition Number Complexity of an Elementary Algorithm for Resolving a Conic Linear System,\u201d with Marina Epelman, Sloan Working Paper # 97-3942, 1997.<\/p>\n

\u201cReasoning with Incomplete Knowledge Using de Finetti\u2019s Fundamental Theorem of Probability: Background and Computational Issues,\u201d with Tracy Myers and Gordon Kaufman, Sloan Working Paper # 97-3990, 1997.<\/p>\n

\u201cComplexity of an Algorithm for Finding an Approximate Solution of a Semi-Definite Program, with no Regularity Condition,\u201d O.R. Center Working Paper 302-94, December 1994. [Working Paper<\/a>]<\/p>\n

\u201cImplementation and Empirical Study of a Combined Phase I - Phase II Potential Reduction Algorithm for Linear Programming,\u201d with Hitendra Wadhwa, Sloan School Working Paper #3411-92-MSA, March 1992. [Working Paper<\/a>]<\/p>\n

\u201cProjective Transformations for Interior Point Methods, Part II: Analysis of An Algorithm for finding the Weighted Center of a Polyhedral System,\u201d O.R. Working Paper 180 88, June 1988. [Working Paper<\/a>]<\/p>\n

\u201cProjective Transformations for Interior Point Methods, Part I: Basic Theory and Linear Programming,\u201d O.R. Working Paper 179 88, June 1988. [Working Paper<\/a>]<\/p>\n

\u201cOptimal Investment in Flexible Manufacturing Capacity, Part II: Computing Solutions,\u201d with C. Fine, Sloan School Working Paper #1803-86, July 1986.<\/p>\n

\u201cHidden Minimum Norm Problems in Quadratic Programming,\u201d Sloan School Working Paper # 1768-86, 1986.<\/p>\n

\u201cIdentifying the Set of Always-Active Constraints in a System of Linear Inequalities by a Single Linear Program,\u201d with R. Roundy and M.J. Todd, Sloan School Working Paper # 1674-85, 1985. [Working Paper<\/a>]<\/p>\n

\u201cOn Kuhn\u2019s Strong Cubical Lemma,\u201d Working Paper #1557-84, Sloan School of Management, M.I.T., 1984.<\/p>\n

\u201cApplications of a Generalization of a Set Intersection Theorem of von Neumann,\u201d Working Paper # 1528-84, Sloan School of Management, M.I.T., 1984.<\/p>\n

\u00a0_<\/span><\/p>\n<\/div><\/div>

Recent Talks (most recent at the top)<\/h2>

\"Level-Set Geometry and the Performance of Restarted-PDHG for Conic LP<\/a>,\" with Zikai Xiong. Presentation ISMP Montreal, July 2024, also Stanford University MS&E Department, July 2024.<\/p>\n

\u201cLevel-Set Geometry and the Performance of Restarted-PDHG for Conic LP,\u201d<\/a> the Spencer C. Schantz Lecture at Lehigh University, Bethlehem, PA, April 11, 2024.<\/p>\n

\u201cLevel-Set Geometry and the Performance of Restarted-PDHG for Conic LP,\u201d<\/a> INORMS Optimization Conference, Rice University, Houston, TX, March 23, 2024.<\/p>\n

\u201cLevel-Set Geometry and the Performance of Restarted-PDHG for Conic LP,\u201d<\/a> OPT4AI Seminar, Georgia Institute of Technology, Atlanta, GA, February 22, 2024.<\/p>\n

\u201cPredictive Business Analytics,\u201d Universidad del Pacifico, Certificate Program in Data Science and Business Analytics, Lima, Peru, November 8-9, 2023.<\/p>\n

\u201cIntroduction to Practical Predictive and Prescriptive Analytics,\u201d\u00a0 Universidad de Chile Master\u2019s Program in Data Science and Business Analytics, Santiago, Chile, November 3-4, 2023.<\/p>\n

\u201cAlgorithms for Business Analytics: Recommender Systems, Fairness, and Efficiency,\u201d MIT Club of Chile, Santiago, Chile, November 2, 2023.<\/p>\n

\u201cImproving the Geometry of (Conic) Linear Optimization Problems for the Primal-Dual Hybrid Gradient Method (PDHG),\u201d<\/a> INFORMS Annual Meeting, Phoenix, AZ, October 17, 2023.<\/p>\n

\u201cImproving the Geometry of (Conic) Linear Optimization Problems for the Primal-Dual Hybrid Gradient Method (PDHG),\u201d<\/a> Princeton University, Princeton, NJ, October 6, 2023.<\/p>\n

\u201cImproving the Geometry of (Conic) Linear Optimization Problems for the Primal-Dual Hybrid Gradient Method (PDHG),\u201d<\/a> AFOSR Mathematical Optimization Annual Program Review, Arlington, VA, August 28-30, 2023<\/p>\n

\"Some Recent Research in First-Order Methods for Linear Programming,\u201d<\/a> Workshop on Optimization in the Big Data Era, Institute for Mathematical Sciences, National University of Singapore, December, 2022.<\/p>\n

\"Using Taylor-Approximated Gradients to Improve the Frank-Wolfe Method for Empirical Risk Minimization,\"<\/a> Workshop on Modern Nonsmooth Optimization, University of Washington, Seattle, August 2022.<\/p>\n

\"Using Taylor-Approximated Gradients to Improve the Frank-Wolfe Method for Empirical Risk Minimization,\"<\/a> International Conference on Continuous Optimization (ICCOPT), Lehigh University, Bethlehem, PA, July 2022.<\/p>\n

\"New Theory and Improved Computational Performance of the Frank-Wolfe Method for Data Science Applications,\u201d<\/a> Distinguished ADSE Seminar Series, City University of Hong Kong, December 2021.<\/p>\n

\u201cNew Theory and Improved Computational Performance of the Frank-Wolfe Method for Data Science Applications<\/a>,\u201d University of Chicago Booth School of Business, November 2021.<\/p>\n

\"Accelerated First-Order Methods for Exascale Simulation and Learning<\/a>,\" with Cuong Nguyen and Jaime Peraire. Presentation, AFOSR Program Review. August 2020<\/p>\n

\"From Stochastic Frank-Wolfe to the Ellipsoid Method: Recent Progress on Practical Optimization in Machine Learning (the Frank-Wolfe Method) and Theoretical Optimization (the Ellipsoid Method)<\/a>\", Webinar on Mathematical Foundations of Data Science, June 2020.<\/p>\n

\"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods<\/a>,\" Duke University, November 2019.<\/p>\n

\"Advanced Prediction Models, and Social Networks\", invited lectures for the MIT and Universidad de Chile Joint Certificate Program in Data Analytics, October, 2019.<\/p>\n

\"Ethics and Fairness in Machine Learning Models and Data-Driven Decision Making\", MIT Alumni Club of Chile, October, 2019.<\/p>\n

\"An Oblivious Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities<\/a>,\" Universaidad de Chile, October 2019.<\/p>\n

\"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods<\/a>,\" Pontificia Universidad Cat\u00f3lica, Santiago, Chile, October 2019.<\/p>\n

\"Accelerated First-Order Methods for Exascale Simulation and Learning<\/a>,\" with Cuong Nguyen and Jaime Peraire. Presentation, AFOSR Program Review. August 2019.<\/p>\n

\u201cAn Oblivious Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities<\/a>,\" with Jourdain Lamperski and Michael Todd. Presentation, ICCOPT Berlin, Germany. August 2019.<\/p>\n

Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,\"<\/a>\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Carnegie Mellon - Tepper, Pittsburgh PA, May, 2019<\/p>\n

\"Generalized Stochastic Frank-Wolfe Algorithm with Stochastic \\Substitute\" Gradient for Structured Convex Optimization,<\/a>\" Haihao (Sean) Lu, Robert M. Freund INFORMS, Phoenix, 2018<\/p>\n

\"Accelerated First-Order Methods for Exascale Simulation and Learning<\/a>,\" Robert M. Freund, Cuong Nguyen, and Jaime Peraire, ASFOR, August 2018<\/p>\n

\"Accelerating Greedy Coordinate Descent Methods<\/a>,\" Lu, Haihao (Sean), Robert M. Freund, and Vahab Morrokni. Presentation ISMP Bordeaux, July 2018<\/p>\n

\"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,\u201d<\/a> Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Pennsylvania State University, State College PA, March 2018<\/p>\n

\"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,<\/a>\" Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, INFORMS Optimization Conference, Denver, CO, March 2018<\/p>\n

\"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods<\/a>,<\/a>\u201d Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, INFORMS Houston, October 2017<\/p>\n

\u201cCondition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,<\/a>\u201d Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, University of Illinois Urbana\/Champaign, September 2017.<\/p>\n

\"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,\u201d<\/a>\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, ISI Marrakech, Morocco, July 2017.<\/p>\n

\"New Results for Sparsity-inducing Methods for Logistic Regression,\" <\/a>Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, SIAM Conference on Optimization, Vancouver, CA, May 2017.<\/p>\n

\u201cAn Extended Frank-Wolfe Method, and its Application to Low-Rank Matrix Completion.\"<\/a>\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, IEEE Conference on Decision and Control, Las Vegas, December 2016.<\/p>\n

\"New Results for Sparsity-inducing Methods for Logistic Regression<\/a>.\" Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Cornell University, Ithaca, NY. November 2016.<\/p>\n

\u201cNew Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure.\"<\/a>\u00a0Freund, Robert M., and Haihao Lu. Presentation, Continuous Optimization: Challenges and Applications, The Technion, Haifa, Israel. September 2016.<\/p>\n

\u201cNew Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure<\/a>.\" Freund, Robert, M., Haihao Lu. Presentation, \u00a0ICCOPT Tokyo, Japan. August 2016.<\/p>\n

\"A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives<\/a>\"\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Princeton University, Princeton, NJ. April 2016.<\/p>\n

\"A New Perspective on Boosting in Linear Regression via Subradient Optimization and Relatives<\/a>.\"\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation,\u00a0Computational and Methodological Statistics Conference, London, UK. December 2015.<\/p>\n

\"An Extended Frank-Wolfe Method, and its\u00a0Application to Low-Rank Matrix Completion<\/a>.\"\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, University of British Columbia, Vancouver, Canada. December 2015.<\/p>\n

\"New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Number<\/a>.\"\u00a0Freund, Robert M., and Haihao Lu. Presentation, INFORMS, Philadelphia, PA. November 2015.<\/p>\n

\"An Extended Frank-Wolfe Method, and is Application to Low-Rank Matrix Completion<\/a>.\" Freund, Robert M. Presentation,\u00a0MIT Stochastics and Statistics Seminar, Cambridge, MA. September 2015.<\/p>\n

\"Extending Renegar's Recent Work: A Different\/Improved Analysis of Basic First-Order Methods in Convex Optimization<\/a>.\" Freund, Robert M. Presentation, ISMP, Pittsburg, PA. July 2015.<\/p>\n

\"Extending Renegar's Recent Work: A Different\/Improved Analysis of Basic First-Order Methods for Conic Optimization<\/a>.\" Freund, Robert M. Presentation,\u00a0Optimization Conference in honor of Tamas Terlaky, HEC, Montreal, Canada. June 2015.<\/p>\n

\"Lectures on Greedy-type Algorith in Convex Optimization<\/a>.\" Freund, Robert M. Presentation, University of Texas, Austin, Texas. November 13, 2015.<\/p>\n

\"An Extended Frank-Wolfe Method, with Applications to Low-Rank Matrix Completion<\/a>.\"\u00a0Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, INFORMS, San Francisco, CA. November 2014.<\/p>\n

\"Mike Todd: Moving Optimzation Forward<\/a>.\" Freund, Robert M. Presentation, Cornell University, Ithaca, NY. August 2014.<\/p>\n

\u201cFirst-Order Methods Yield New Analysis and Results for Boosting Methods in Statistics\/Machine Learning<\/a>.\" Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, SIOPT Meeting, San Diego, CA. May 2014.<\/p>\n

\u201cA First-Order View of Some Boosting Methods: Computational Guarantees and Connections to Regularization<\/a>.\" Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation,\u00a0Cornell University, Ithaca, NY. March 2014.<\/p>\n

\u201cThe Frank-Wolfe Algorithm: New Results, and Connections to Statistical Boosting<\/a>.\u201d Grigas, Paul, Robert Freund, and Rahul Mazumder. Presentation,\u00a0Workshop on Optimization and Big Data, University of Edinburgh, Scotland. May 2013.<\/p>\n

\u201cAn Optimizer's View of Statistical Boosting Algorithms<\/a>.\u201d Freund, Robert, Paul Grigas, and Rahul Mazumder. Presentation,\u00a0ICHOI, Chilean Institute of Operations Research. April 2013.<\/p>\n

\u201cFabrication-Adaptive Optimization, with an Application to Photonic Crystal Design<\/a>.\u201d Men, Han, Joel Saa-Seoane, Ngoc Cuong Nguyen, Robert M. Freund, and Jaime Peraire.\u00a0Georgia Institute of Technology. January 2013.<\/p>\n

\u201cImplementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Bandgaps<\/a>.\u201d Men, Han, Joel Saa-Seoane, Ngoc Cuong Nguyen, Robert Freund, and Jaime Peraire. Presentation,\u00a0Sabanci University, Istanbul, Turkey. August 2012.<\/p>\n

\u201cIllustrations of Business Analytics and the 21st Century Industrial Revolution<\/a>.\" Freund, Robert M. Presentation, Sabanci University, Istanbul, Turkey.\u00a0October 2012.<\/p>\n

\u201cProximal Subgradient and Dual Averaging for Sequential Decision-making and Non-smooth Optimization<\/a>.\" Grigas, Paul, and Robert M. Freund. Presentation, ISMP, Berlin, Germany. August 2012.<\/p>\n

\u201cImplementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Bandgaps<\/a>.\u201dMen, Han, Joel Saa-Seoane, Ngoc Cuong Nguyen, Robert M. Freund, and Jaime Peraire. Presentation, ISMP, Berlin, Germany. August 2012.<\/p>\n

\u201cRecent Research on Design Optimization of Wave Propagation in Metamaterials: Fabrication-Robust Design, and Binary Optimization with Reduced Basis<\/a>.\u201d Men, Han, Ngoc Cuong Nguyen, Joel Saa-Seoane, Robert M. Freund, and Jaime Peraire. Presentation,\u00a0AFOSR Optimization and Discrete Mathematics Program Review. April 2012.<\/p>\n

\u201cImplementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Multiple and Complete Bandgaps<\/a>.\u201d Men, Han, Ngoc Cuong Nguyen, Joel Saa-Seoane, Robert M. Freund, and Jaime Peraire. Presentation,\u00a0Catolica University, Santiago, Chile. March 2012.<\/p>\n

\u201cBandgap Optimization of Photonic Crystals via Semidefinite Programming and Subspace Methods.<\/a>\u201d Freund, Robert M., Han Men, Joel Saa-Seoane, Ngoc Cuong Nguyen, Pablo Parillo, and Jaime Peraire. Presentation,\u00a0Fields Institute Conference on Discrete Geometry and Optimization, Toronto, Canada, September 2011 and SIAM Conference on Optimization, Darmstadt, Germany. May 2011.<\/p>\n

\u201cDesign of Photonic Crystals with Multiple and Combined Band Gaps, plus Fabrication-Robust Design<\/a>.\u201d Freund, Robert M., Han Men, Ngoc Cuong Nguyen, Pablo Parrilo, and Jaime Peraire. Presentation,\u00a0AFOSR. April 2011.<\/p>\n

\u201cBand Gap Optimization of 2-Dimensional Photonic Crystals using Semi-Definite Programming and Subspace Methods<\/a>.\u201d Freund, Robert M., Han Men, Ngoc Cuong Nguyen, Pablo Parrilo, and Jaime Peraire. Presentation,\u00a0ICCOPT 2010, Santiago. July 2010.<\/p>\n

\u201cPrimal-Dual Geometry of Level Sets and their Explanatory Value of the Practical Performance of Interior-Point Methods for Conic Optimization<\/a>.\u201d Freund, Robert M. Presentation, Fields Institute, Toronto, Canada. June 2010.<\/p>\n

\u201cBehavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems<\/a>.\u201d Freund, Robert M., Fernando Ord\u00f3\u00f1e, and Kim-Chuan Toh. Presentation,\u00a0Cambridge University Judge School of Business, Cambridge, UK. November, 2009.<\/p>\n

\u201cPrimal-Dual Geometry of Level Sets and their Explanatory Value of the Practical Performance of Interior-Point Methods for Conic Optimization<\/a>.\u201d Freund, Robert M., Presentation, ETH Zurich, Switzerland. November 2009.<\/p>\n

\u201cOn the Primal-Dual Geometry of Level Sets in Linear and Conic Convex Optimization<\/a>.\u201d Freund, Robert M. Presentation, INFORMS Annual Meeting, San Diego, CA. October 2009.<\/p>\n

\u201cEquivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model<\/a>.\u201d Freund, Robert M., and Jorge Vera. Presentation, International Symposium on Mathematical Programming, Chicago, IL. August 2009.<\/p>\n

\u201cImproved Initialization of the Homogeneous Self-Dual Embedding Model for Solving Conic Convex Optimization<\/a>.\u201d Belloni, Alexandre, Robert M. Freund, Kim-Chuan Toh, and Allison Chang. Presentation,\u00a0SIAM Conference on Optimization, Boston, MA. May 2008.<\/p>\n

\u201cDesigning and Delivering a Better Management Science Course for MBA Students<\/a>.\u201d Freund, Robert M. Presentation, INFORMS Annual Meeting, Seattle, WA. November, 2007.<\/p>\n

\u201cRandomized Methods for Solving Convex Problems: Some Theory and Some Computational Experience<\/a>.\u201d Freund, Robert M., and Alexandre Belloni. Presentation. University of Southern California, Los Angeles, CA. October, 2007.<\/p>\n

\u201cProjective Re-Normalization for Improving the Performance of IPMs for Conic Optimization<\/a>.\u201d Belloni, Alexandre, and Robert M. Freund. Presentation,\u00a0ICCOPT-2, Hamilton, Canada. August, 2007.<\/p>\n

\u201cOn Efficient Randomized Methods for Convex Optimization<\/a>.\u201d Freund, Robert M. Presentation, Banff International Research Station,\u00a0Banff, Canada. November 2006.<\/p>\n

\u201cBehavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems<\/a>.\u201d Freund, Robert M., Fernando Ord\u00f3\u00f1ez, and Kim-Chuan Toh. Presentation,\u00a0Northwestern University, Evanstown, IL. October 2006.<\/p>\n

\u201cEfficiency of a Re-scaled Perceptron Algorithm for Conic Systems<\/a>.\u201d Belloni, Alexandre, Robert M. Freund, and Santosh Vempala. Presentation,\u00a0International Symposium on Mathematical Programming, Rio de Janeiro, Brazil. August 2006.<\/p>\n

\u201cEfficiency of a Re-scaled Perceptron Algorithm for Conic Systems<\/a>.\u201d Belloni, Alexandre, Robert M. Freund, and Santosh Vempala, 9th International Workshop on High Performance Optimization Techniques, Delft, The Netherlands. June 2006.<\/p>\n

\u201cProjective Pre-Conditioners for Improving the Behavior of a Conic Inequality System<\/a>.\u201d Freund, Robert M., and Alexandre Belloni. Presentation, Cowles Foundation Conference on Optimization, Yale University, New Haven, CT. March 2006.<\/p>\n

\u201cProjective Pre-Conditioners for Improving the Behavior of a Linear or Conic Inequality System<\/a>.\u201d Freund, Robert M., and Alexandre Belloni. Presentation,\u00a0MIT Mathematics Department Applied Mathematics Colloquium, Cambridge, MA. February 2006.<\/p>\n

\u201cReducing the Solution Time for Convex Optimization Problems by Pre-Conditioning Transformations<\/a>.\u201d Freund, Robert M., and Alexandre Belloni. Presentation,\u00a0Singapore-MIT Alliance Symposium, Singapore. January 2006.<\/p>\n

\u201cRandomized Methods for (Continuous) Deterministic Optimization and Associated Complexity Analysis<\/a>.\u201d Freund, Robert M., and Alexandre Belloni. Presentation, Stanford University, Stanford, CA. October 2005.<\/p>\n

\u201cRandomized Methods for (Continuous) Deterministic Optimization and Associated Complexity Analysis<\/a>.\u201d Belloni, Alexandre, and Robert M. Freund. Presentation,\u00a0Foundations of Computational Mathematics, Santander, Spain. July 2005.<\/p>\n

\u201cProjective Pre-Conditioners for Improving the Behavior of a Homogeneous Conic Linear System<\/a>.\u201d Belloni, Alexandre, and Robert M. Freund. Presentation, SIAM Conference on Optimization, Stockholm, Sweden. May 2005.<\/p>\n

\u201cOn the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization<\/a>.\u201d Freund, Robert M. Presentation,\u00a0SIAM Conference on Optimization, Stockholm, Sweden. May 2005.<\/p>\n

\u201cOn the Causes of Variability in IPM Iterations on Semi-Definite Programming Problems<\/a>.\u201d Freund, Robert M., Fernando Ord\u00f3\u00f1ez and Kim-Chuan Toh. Presentation,\u00a0SIAM Conference on Optimization, Stockholm, Sweden. May 2005.<\/p>\n

\u201cOn the Symmetry Function of a Convex Set<\/a>.\u201d Belloni, Alexandre, and Robert M. Freund. Presentation, Workshop on Large Scale Nonlinear and Semidefinite Programming, University of Waterloo, Waterloo, Ontario. June 2004.<\/p>\n

\u201cComputational Experience and the Explanatory Value of Condition Numbers for Linear Optimization<\/a>.\u201d Freund, Robert M., and Fernando Ord\u00f3\u00f1ez. Presentation, Lehigh University, Bethlehem, PA. April 2003.<\/p>\n

_<\/span><\/p>\n<\/div><\/div>

Current and Former Students and Co-Authors<\/h2>