### Publications (most recent at the top)

"Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods" Freund, R.M., P. Grigas, and R. Mazumder, *submitted.*

"Generalized Stochastic Frank-Wolfe Algorithm with Stochastic “Substitute” Gradient for Structured Convex Optimization" Lu, Haihao, and Robert M. Freund, *submitted*.

"Accelerating Greedy Coordinate Descent Methods," Lu, Haihao, Robert M. Freund, and Vahab Morrokni, to appear at International Conference on Machine Learning (ICML) 2018, Stockholm. ICML Version. Supplementary Material.

"Accelerated Residual Descent Methods For the Iterative Solutions of Systems of Equations," Nguyen, Ngoc Cuong, P. Fernandez, R.M. Freund, and J. Peraire, *SIAM Journal of Scientific Computing (2018), vol. 40 (5) ppA3157-A3179*

"Relatively-Smooth Convex Optimization by First-Order Methods, and Applications," Lu, Haihao, Robert M. Freund, and Yurii Nesterov, *SIAM Journal on Optimization* (2018), vol. 28 (I) pp. 333-354

"An Extended Frank-Wolfe Method with "In-Face" Directions, and its Application to Low-Rank Matrix Completion" Freund, Robert M., Paul Grigas, and Rahul Mazumder. *SIAM Journal on Optimization (2017), 1, pp 319-346*.

"New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure," Freund, Robert M., and Haihao Lu, *Mathematical Programming. Ser. A (2018) 170:445-477*

"A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives." Freund, Robert M., Paul Grigas and Rahul Mazumder. *Annals of Statistics*, Vol. 45, No. 6, (2017): 2328-2364 , Supplementary Material Document

“Functional Regression for State Prediction Using Linear PDE Models and Observations.” Nguyen, Ngoc Cuong, Han Men, Robert M. Freund, and Jaime Peraire. *SIAM Journal on Scientific Computing* Vol. 38, No. 2 (2016): B247-B271.

“Robust topology optimization of three-dimensional photonic-crystal band-gap structures.” Men, Han, Karen Y. K. Lee, Robert M. Freund, Jaime Peraire and Steven G. Johnson. *Optics Express** *Vol. 22, No. 19 (2014): 22632-22648.

“Designing Phononic Crystals with Conic Convex Optimization.” Han Men, Ngoc C. Nguyen, Joel Saa-Seoane, Robert M. Freund and Jaime Peraire. In *ASME2013 International Mechanical Engineering Congress and Exposition: Volume 14, Vibration, Acoustics and Wave Propagation.* San Diego, CA: November 2013.

“New Analysis and Results for the Frank-Wolfe Method.” Freund, Robert M., and Paul Grigas. *Mathematical Programming *155 (1), pp. 199-230, January 2016.

“AdaBoost and Forward Stagewise Regression are First-Order Convex Optimization Methods.” Freund, Robert M., Paul Grigas, and Rahul Mazumder, MIT Operations Research Center Working Paper 397-14. March 2014.

"Bandwidth Optimization of Single-Polarization Single-Mode Photonic Crystal Fibers." Han Men, Ngoc Cuong Nguyen, Robert M. Freund, and Jaime Peraire. Technical Report. 2013.

“Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design." Men, Han, Robert M. Freund, Ngoc Cuong Nguyen, Joel Saa-Seoane, and Jaime Peraire. *Operations Research** *Vol. 62, No. 2 (2014): 418-434.

“A Binary Optimization Method for for Linear PDE-governed Material Design.” Saa-Seoane, Joel, Ngoc Cuong Nguyen, Han Men, Robert M. Freund, and Jaime Peraire. *Journal of Applied Physics A** *Vol. 109, No. 4 (2012): 1023-1030.

“An Accelerated First-Order Method for Solving Unconstrained SOS Polynomial Optimization Problems.” Bertsimas, Dimitris, Robert M. Freund, and Xu Andy Sun. *Optimization Methods and Software** *Vol. 28, No. 3 (2013): 424-441.

“Design of Photonic Crystals with Multiple and Combined Band Gaps.” Men, Han., Ngoc Cuong Nguyen, Robert M. Freund, Kian-Meng Lim, Pablo Parrilo and Jaime Peraire. *Physical Review E** *Vol. 85, No. 4 (2012): 1-8.

“Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods." Men, Han, Ngoc C. Nguyen, Robert M. Freund, Pablo A. Parrilo and Jaime Peraire. *Journal of Computational Physics* Vol. 229, No. 10 (2010): 3706–3725.

“Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model.” Freund, Robert M., and Jorge Vera. *Mathematics of Operations Research** *Vol. 34, No.4 (2009): 869-879.

“A Geometric Analysis of Renegar’s Condition Number, and its Interplay with Conic Curvature.” Belloni, Alexandre and Robert M. Freund. *Mathematical Programming** *Vol. 119, No. 1 (2009): 95-107.

“On the Second-Order Feasibility Cone: Primal-Dual Representation and Efficient Projection.” Belloni, Alexandre and Robert M. Freund. *SIAM Journal on Optimization** *Vol. 19, No.3 (2008): 1073-1092.

“An Efficient Re-Scaled Perceptron Algorithm for Conic Systems.” Belloni, Alexandre, Robert M. Freund and Santosh Vempala,* **Mathematics of Operations Research** *Vol. 34, No. 3 (2009): 621-641.

“Projective Re-Normalization for Improving the Behavior of a Homogeneous Conic Linear System.” Belloni, Alexandre and Robert M. Freund. *Mathematical Programming** *Vol. 118, No. 2 (2009): 279-299.

“Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems.” Freund, Robert M., Fernando Ordóñez, and Kim Chuan Toh. *Mathematical Programming* Vol. 109, No. 2 (2007): 445-475.

"Optimizing Product Line Designs: Efficient Methods and Comparisons." Belloni, Alexandre, Robert Freund, Matthew Selove and Duncan Simester. *Management Science** *Vol. 54, No. 9 (2008): 1544-1553.

“On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization.” Freund, Robert M. *Mathematical Programming** *Vol. 106, No. 3 (2006): 527-545.

“On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems.” Cai, Zhi, and Robert M. Freund. *Computational Optimization and Applications* Vol. 34, No. 3 (2006): 299-320.

“On the Symmetry Function of a Convex Set.” Belloni, Alexandre, and Robert M. Freund. *Mathematical Programming* Vol. 111, No. 1 (2008): 57-93.

“On an Extension of Condition Number Theory to Nonconic Convex Optimization.” Freund, Robert M. and Fernando Ordóñez. *Mathematics of Operations Research** *Vol. 30, No. 1 (2005): 173-194.

“Computation of Minimum Volume Covering Ellipsoids.” Sun, Peng, and Robert M. Freund. *Operations Research* Vol. 52, No. 5 (2004): 690-706.

“Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization.” Ordóñez, Fernando, and Robert M. Freund. *SIAM Journal on Optimization** *Vol. 14, No. 2 (2004) 307-333.

“Solution Methodologies for the Smallest Enclosing Circle Problem.” Xu, Sheng, Robert M. Freund, and Jie Sun. *Computational Optimization and Applications** *Vol. 25, No. 1 (2003): 283-292.

“Complexity of Convex Optimization using Geometry-Based Measures and a Reference Point.” Freund, Robert M. *Mathematical Programming** *Vol. 99, No. 2 (2004): 197-221.

“On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization.” Freund, Robert M. *SIAM Journal on Optimization** *Vol. 13, No. 4 (2003): 1004-1013.

“A new condition measure, pre-conditioners, and relations between different measures of conditioning for conic linear systems.” Epelman, Marina, and Robert M. Freund. *SIAM Journal on Optimization** *Vol. 12, No. 3 (2002): 627-655.

“On the Complexity of Computing Estimates of Condition Measures of a Conic Linear System.” Freund, Robert M. and Jorge R. Vera. *Mathematics of Operations Research** *Vol. 28, No. 4 (2003): 625-648.

"Condition-Measure Bounds on the Behavior of the Central Trajectory of a SemiDefinite Program." Nunez, Manuel A., and Robert M. Freund. *SIAM Journal on Optimization** *Vol. 11, No. 3 (2001): 818-836.

“Condition Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm.” Freund, Robert M., and Jorge R. Vera. *SIAM Journal on Optimization** *Vol. 10, No. 1 (1999): 155-176.

“Condition Number Complexity of an Elementary Algorithm for Computing a Reliable Solution of a Conic Linear System.” Epelman, Marina, and Robert M. Freund. *Mathematical Programming** *Vol. 88, No. 3 (2000): 451-485.

“Condition Number Complexity of an Elementary Algorithm for Resolving a Conic Linear System.” Epelman, Marina and Robert M. Freund, MIT Sloan Working Paper 97-3942. 1997.

“Interior Point Methods: Current Status and Future Directions.” Freund, Robert M., and Shinji Mizuno. In *High Performance Optimization** *, edited by Hans Frenk, Kees Roos, Tamas Terlaky, and Shuzhong Zhang, 441-446. New York, NY: Springer Science + Business Media, 2000.

“Condition Measures and Properties of the Central Trajectory of a Linear Program.” Nunez, Manuel A., and Robert M. Freund. *Mathematical Programming** *Vol. 83, No. 1 (1998): 1-28.

“Some Characterizations and Properties of the ‘Distance to Ill-Posedness’ and the Condition Measure of a Conic Linear System.” Freund, Robert M., and Jorge R. Vera. *Mathematical Programming** *Vol. 86, No. 2 (1999): 225-260.

“Training Support Vector Machines: an Application to Face Detection.” Edgar Osuna, Robert M. Freund, and Federico Girosi. In *Proceedings of 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition*, edited by Deborah Plummer and Ian Torwick. Los Alamitos, CA: June 1997.

“An Improved Training Algorithm for Support Vector Machines.” Edgar Osuna, Robert M. Freund, and Federico Girosi. In *Neural Networks for Signal Processing VII:* *Proceedings of the 1997 IEEE Signal Processing Society Workshop*, edited by Jose Principe, Lee Gile, Nelson Morgan and Elizabeth Wilson. New York, NY: September 1997.

“Complexity of an Algorithm for Finding an Approximate Solution of a SemiDefinite Program, with no Regularity Condition.” Freund, Robert M., MIT Operations Research Center Working Paper 302-94. December 1995.

“An Infeasible-Start Algorithm for Linear Programming whose Complexity Depends on the Distance from the Starting Point to the Optimal Solution.” Freund, Robert M. *Annals of Operations Research** *Vol. 62, No. 1 (1996): 29-58.

“Following a 'Balanced' Trajectory from an Infeasible Point to an Optimal Linear Programming Solution with a Polynomial-time Algorithm.” Freund, Robert M. *Mathematics of Operations Research** *Vol. 21, No.4 (1996): 839-859.

“Barrier Functions and Interior-Point Algorithms for Linear Programming with Zero, One-, or Two-Sided Bounds on the Variables.” Freund, Robert M., and Michael J. Todd. *Mathematics of Operations Research** *Vol. 20, No. 2 (1995): 415-440.

“A Potential Reduction Algorithm with User-specified Phase I - Phase II Balance, for Solving a Linear Program from an Infeasible Warm Start.” Freund, Robert M. *SIAM Journal of Optimization** *Vol. 5, No.2 (1995): 247-268.

“Prior Reduced Fill-In in Solving Equations in Interior-Point Algorithms.” Birge, John R., Robert M. Freund, and Robert Vanderbei. *Operations Research Letters** *Vol. 11, No.4 (1992): 195-198.

“Implementation and Empirical Study of a Combined Phase I - Phase II Potential Reduction Algorithm for Linear Programming.” Freund, Robert M., and Hitendra Wadhwa, MIT Sloan Working Paper 3411-92-MSA. March 1992.

“A Potential Function Reduction Algorithm for Solving a Linear Program Directly from an Infeasible 'Warm Start.'” Freund, Robert M. *Mathematical Programming** *Vol. 52, No.1 (1991): 441-466.

“Projective Transformation for Interior-Point Algorithms, and a Superlinearly Convergent Algorithm for the W-Center Problem.” Freund, Robert M. *Mathematical Programming** *Vol. 58, No.1 (1993): 385-414.

“A Method for the Parametric Center Problem, with a Strictly Monotone Polynomial-Time Algorithm for Linear Programming.” Freund, Robert M., and Kok-Choon Tan. *Mathematics of Operations Research** *Vol. 16, No. 4 (1991): 775-801.

“Theoretical Efficiency of a Shifted Barrier Function Algorithm for Linear Programming.” Freund, Robert M. *Linear Algebra and its Applications** *Vol. 152, No. 1 (1991): 19-41.

“Polynomial-Time Algorithms for Linear Programming based only on Primal Scaling and Projected Gradients of a Potential Function.” Freund, Robert M. *Mathematical Programming** *Vol. 51, No. 1 (1991): 203-222.

“Projective Transformations for Interior Point Methods, Part II: Analysis of An Algorithm for finding the Weighted Center of a Polyhedral System.” Freund, Robert M., MIT Operations Research Center Working Paper 180-88. Cambridge, MA: MIT Operations Research Center, June 1988.

“Projective Transformations for Interior Point Methods, Part I: Basic Theory and Linear Programming.” Freund, Robert M., MIT Operations Research Center Working Paper 179-88. June 1988.

“Optimal Investment in Product Flexible Manufacturing Capacity.” Fine, Charles H., and Robert M. Freund. *Management Science** *Vol. 36, No. 4 (1990): 449-466.

“Combinatorial Analogs of Brouwer’s Fixed Point Theorem on a Bounded Polyhedron.” Freund, Robert M. *Journal of Combinatorial Theory, Series B** *Vol. 47, No. 2 (1989): 192-219.

“An Analog of Karmarkar’s Algorithm for Inequality Constrained Linear Programs, with a 'New' Class of Projective Transformations for Centering a Polytope.” Freund, Robert M. *Operations Research Letters** *Vol. 7, No. 1 (1988): 9–14.

“Identifying the Set of Always-Active Constraints in a System of Linear Inequalities by a Single Linear Program.” Freund, Robert M., Robin Roundy, and Michael J. Todd. MIT Sloan Working Paper 1674-85. Cambridge, MA: MIT Sloan School of Management, October 1985.

“Dual Gauge Programs, with Applications to Quadratic Programming and the Minimum Norm Problem.” Freund, Robert M. *Mathematical Programming** *Vol. 38, No. 1 (1987): 47–68.

“Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube.” Freund, Robert M. *Mathematics of Operations Research** *Vol. 11, No. 1 (1986): 169-179.

"Postoptimal Analysis of a Linear Program Under Simultaneous Changes in Matrix Coefficients." Freund, Robert M. In *Mathematical Programming Essays in Honor of George B. Dantzig Part I*, edited by Richard W. Cottle, 1-13. Amsterdam, Netherlands: North Holland Publishing Company, 1985.

“On the Complexity of Four Polyhedral Set Containment Problems.” Freund, Robert M., and James B. Orlin. *Mathmatical Programming** *Vol. 33, No. 2 (1985): 133-145.

“Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology.” Freund, Robert M. *Mathematics of Operations Research** *Vol. 9, No. 4 (1984): 498-509.

“Variable Dimension Complexes, Part I: Basic Theory.” Freund, Robert M. *Mathematics of Operations Research** *Vol. 9, No. 4 (1984): 479-497.

“Optimal Scaling of Balls and Polyhedra." Eaves, B.C. and Robert M. Freund. *Mathematical Programming** *Vol. 23, No.1 (1982): 138-147.

“A Constructive Proof of Tucker’s Combinatorial Lemma.” Freund, Robert M., and Michael J. Todd. *Journal of Combinatorial Theory* Vol. 30, No. 3 (1981): 321-325.

_

### Recent Talks (most recent at the top)

Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods," Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Carnegie Mellon - Tepper, Pittsburgh PA, May, 2019

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

"Accelerated First-Order Methods for Exascale Simulation and Learning," Robert M. Freund, Cuong Nguyen, and Jaime Peraire, ASFOR, August 2018

"Accelerating Greedy Coordinate Descent Methods," Lu, Haihao (Sean), Robert M. Freund, and Vahab Morrokni. Presentation ISMP Bordeaux, July 2018

"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,” Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Pennsylvania State University, State College PA, March 2018

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

"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,” Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, INFORMS Houston, October 2017

“Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,” Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, University of Illinois Urbana/Champaign, September 2017.

"Condition Number Analysis of Logistic Regression, and its Implications for First-Order Solution Methods,” Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, ISI Marrakech, Morocco, July 2017.

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

“An Extended Frank-Wolfe Method, and its Application to Low-Rank Matrix Completion." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, IEEE Conference on Decision and Control, Las Vegas, December 2016.

"New Results for Sparsity-inducing Methods for Logistic Regression." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Cornell University, Ithaca, NY. November 2016.

“New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure." Freund, Robert M., and Haihao Lu. Presentation, Continuous Optimization: Challenges and Applications, The Technion, Haifa, Israel. September 2016.

“New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure." Freund, Robert, M., Haihao Lu. Presentation, ICCOPT Tokyo, Japan. August 2016.

"A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives" Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Princeton University, Princeton, NJ. April 2016.

"A New Perspective on Boosting in Linear Regression via Subradient Optimization and Relatives." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Computational and Methodological Statistics Conference, London, UK. December 2015.

"An Extended Frank-Wolfe Method, and its Application to Low-Rank Matrix Completion." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, University of British Columbia, Vancouver, Canada. December 2015.

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

"An Extended Frank-Wolfe Method, and is Application to Low-Rank Matrix Completion." Freund, Robert M. Presentation, MIT Stochastics and Statistics Seminar, Cambridge, MA. September 2015.

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

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

"Lectures on Greedy-type Algorith in Convex Optimization." Freund, Robert M. Presentation, University of Texas, Austin, Texas. November 13, 2015.

"An Extended Frank-Wolfe Method, with Applications to Low-Rank Matrix Completion." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, INFORMS, San Francisco, CA. November 2014.

"Mike Todd: Moving Optimzation Forward." Freund, Robert M. Presentation, Cornell University, Ithaca, NY. August 2014.

“First-Order Methods Yield New Analysis and Results for Boosting Methods in Statistics/Machine Learning." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, SIOPT Meeting, San Diego, CA. May 2014.

“A First-Order View of Some Boosting Methods: Computational Guarantees and Connections to Regularization." Freund, Robert M., Paul Grigas, and Rahul Mazumder. Presentation, Cornell University, Ithaca, NY. March 2014.

“The Frank-Wolfe Algorithm: New Results, and Connections to Statistical Boosting.” Grigas, Paul, Robert Freund, and Rahul Mazumder. Presentation, Workshop on Optimization and Big Data, University of Edinburgh, Scotland. May 2013.

“An Optimizer's View of Statistical Boosting Algorithms.” Freund, Robert, Paul Grigas, and Rahul Mazumder. Presentation, ICHOI, Chilean Institute of Operations Research. April 2013.

“Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design.” Men, Han, Joel Saa-Seoane, Ngoc Cuong Nguyen, Robert M. Freund, and Jaime Peraire. Georgia Institute of Technology. January 2013.

“Implementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Bandgaps.” Men, Han, Joel Saa-Seoane, Ngoc Cuong Nguyen, Robert Freund, and Jaime Peraire. Presentation, Sabanci University, Istanbul, Turkey. August 2012.

“Illustrations of Business Analytics and the 21st Century Industrial Revolution." Freund, Robert M. Presentation, Sabanci University, Istanbul, Turkey. October 2012.

“Proximal Subgradient and Dual Averaging for Sequential Decision-making and Non-smooth Optimization." Grigas, Paul, and Robert M. Freund. Presentation, ISMP, Berlin, Germany. August 2012.

“Implementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Bandgaps.”Men, Han, Joel Saa-Seoane, Ngoc Cuong Nguyen, Robert M. Freund, and Jaime Peraire. Presentation, ISMP, Berlin, Germany. August 2012.

“Recent Research on Design Optimization of Wave Propagation in Metamaterials: Fabrication-Robust Design, and Binary Optimization with Reduced Basis.” Men, Han, Ngoc Cuong Nguyen, Joel Saa-Seoane, Robert M. Freund, and Jaime Peraire. Presentation, AFOSR Optimization and Discrete Mathematics Program Review. April 2012.

“Implementation-Robust Design: Modeling, Theory, and Application to Photonic Crystal Design with Multiple and Complete Bandgaps.” Men, Han, Ngoc Cuong Nguyen, Joel Saa-Seoane, Robert M. Freund, and Jaime Peraire. Presentation, Catolica University, Santiago, Chile. March 2012.

“Bandgap Optimization of Photonic Crystals via Semidefinite Programming and Subspace Methods.” Freund, Robert M., Han Men, Joel Saa-Seoane, Ngoc Cuong Nguyen, Pablo Parillo, and Jaime Peraire. Presentation, Fields Institute Conference on Discrete Geometry and Optimization, Toronto, Canada, September 2011 and SIAM Conference on Optimization, Darmstadt, Germany. May 2011.

“Design of Photonic Crystals with Multiple and Combined Band Gaps, plus Fabrication-Robust Design.” Freund, Robert M., Han Men, Ngoc Cuong Nguyen, Pablo Parrilo, and Jaime Peraire. Presentation, AFOSR. April 2011.

“Band Gap Optimization of 2-Dimensional Photonic Crystals using Semi-Definite Programming and Subspace Methods.” Freund, Robert M., Han Men, Ngoc Cuong Nguyen, Pablo Parrilo, and Jaime Peraire. Presentation, ICCOPT 2010, Santiago. July 2010.

“Primal-Dual Geometry of Level Sets and their Explanatory Value of the Practical Performance of Interior-Point Methods for Conic Optimization.” Freund, Robert M. Presentation, Fields Institute, Toronto, Canada. June 2010.

“Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems.” Freund, Robert M., Fernando Ordóñe, and Kim-Chuan Toh. Presentation, Cambridge University Judge School of Business, Cambridge, UK. November, 2009.

“Primal-Dual Geometry of Level Sets and their Explanatory Value of the Practical Performance of Interior-Point Methods for Conic Optimization.” Freund, Robert M., Presentation, ETH Zurich, Switzerland. November 2009.

“On the Primal-Dual Geometry of Level Sets in Linear and Conic Convex Optimization.” Freund, Robert M. Presentation, INFORMS Annual Meeting, San Diego, CA. October 2009.

“Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model.” Freund, Robert M., and Jorge Vera. Presentation, International Symposium on Mathematical Programming, Chicago, IL. August 2009.

“Improved Initialization of the Homogeneous Self-Dual Embedding Model for Solving Conic Convex Optimization.” Belloni, Alexandre, Robert M. Freund, Kim-Chuan Toh, and Allison Chang. Presentation, SIAM Conference on Optimization, Boston, MA. May 2008.

“Designing and Delivering a Better Management Science Course for MBA Students.” Freund, Robert M. Presentation, INFORMS Annual Meeting, Seattle, WA. November, 2007.

“Randomized Methods for Solving Convex Problems: Some Theory and Some Computational Experience.” Freund, Robert M., and Alexandre Belloni. Presentation. University of Southern California, Los Angeles, CA. October, 2007.

“Projective Re-Normalization for Improving the Performance of IPMs for Conic Optimization.” Belloni, Alexandre, and Robert M. Freund. Presentation, ICCOPT-2, Hamilton, Canada. August, 2007.

“On Efficient Randomized Methods for Convex Optimization.” Freund, Robert M. Presentation, Banff International Research Station, Banff, Canada. November 2006.

“Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems.” Freund, Robert M., Fernando Ordóñez, and Kim-Chuan Toh. Presentation, Northwestern University, Evanstown, IL. October 2006.

“Efficiency of a Re-scaled Perceptron Algorithm for Conic Systems.” Belloni, Alexandre, Robert M. Freund, and Santosh Vempala. Presentation, International Symposium on Mathematical Programming, Rio de Janeiro, Brazil. August 2006.

“Efficiency of a Re-scaled Perceptron Algorithm for Conic Systems.” Belloni, Alexandre, Robert M. Freund, and Santosh Vempala, 9th International Workshop on High Performance Optimization Techniques, Delft, The Netherlands. June 2006.

“Projective Pre-Conditioners for Improving the Behavior of a Conic Inequality System.” Freund, Robert M., and Alexandre Belloni. Presentation, Cowles Foundation Conference on Optimization, Yale University, New Haven, CT. March 2006.

“Projective Pre-Conditioners for Improving the Behavior of a Linear or Conic Inequality System.” Freund, Robert M., and Alexandre Belloni. Presentation, MIT Mathematics Department Applied Mathematics Colloquium, Cambridge, MA. February 2006.

“Reducing the Solution Time for Convex Optimization Problems by Pre-Conditioning Transformations.” Freund, Robert M., and Alexandre Belloni. Presentation, Singapore-MIT Alliance Symposium, Singapore. January 2006.

“Randomized Methods for (Continuous) Deterministic Optimization and Associated Complexity Analysis.” Freund, Robert M., and Alexandre Belloni. Presentation, Stanford University, Stanford, CA. October 2005.

“Randomized Methods for (Continuous) Deterministic Optimization and Associated Complexity Analysis.” Belloni, Alexandre, and Robert M. Freund. Presentation, Foundations of Computational Mathematics, Santander, Spain. July 2005.

“Projective Pre-Conditioners for Improving the Behavior of a Homogeneous Conic Linear System.” Belloni, Alexandre, and Robert M. Freund. Presentation, SIAM Conference on Optimization, Stockholm, Sweden. May 2005.

“On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization.” Freund, Robert M. Presentation, SIAM Conference on Optimization, Stockholm, Sweden. May 2005.

“On the Causes of Variability in IPM Iterations on Semi-Definite Programming Problems.” Freund, Robert M., Fernando Ordóñez and Kim-Chuan Toh. Presentation, SIAM Conference on Optimization, Stockholm, Sweden. May 2005.

“On the Symmetry Function of a Convex Set.” Belloni, Alexandre, and Robert M. Freund. Presentation, Workshop on Large Scale Nonlinear and Semidefinite Programming, University of Waterloo, Waterloo, Ontario. June 2004.

“Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization.” Freund, Robert M., and Fernando Ordóñez. Presentation, Lehigh University, Bethlehem, PA. April 2003.

_

### Current and Former Students and Co-Authors

- Alexandre Belloni
- Dimitris Bertsimas
- John Birge
- Zhi Cai
- Curtis Eaves
- Marina Epelman
- Charles Fine
- Federico Girosi
- Paul Grigas
- Rahul Mazumder
- Abby Men
- Shinji Mizuno
- Vahab Mirrokni
- Yurii Nesterov
- Ngoc Cuong Nguyen
- Manuel Nunez
- Fernando Ordóñez
- James Orlin
- Edgar Osuna
- Pablo Parrilo
- Jaime Peraire
- Robin Roundy
- Joel Saa-Seoane
- Matthew Selove
- Xu Sheng
- Duncan Simester
- Jie Sun
- Andy Sun
- Peng Sun
- Kok Choon Tan
- Michael Todd
- Kim Chuan Toh
- Robert Vanderbei
- Santosh Vempala
- Jorge Vera