Robert Freund

Theresa Seley Professor of Management Science
Professor of Operations Research

Biography | Selected Publications

New Analysis and Results for the Frank-Wolfe Method.” Freund, Robert M. and Paul Grigas. Mathematical Programming. Forthcoming.

""A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives." Freund, Robert M., Paul Grigas and Rahul Mazumder, Working Paper. May 2015.

“Gaussian Functional Regression for Linear Partial Differential Equations.” Nguyen, Ngoc C., Han Men, Robert M. Freund and Jaime Peraire. Computer Methods in Applied Mathematics and Engineering Vol. 287, No. 15 (2015): 69-89. (2015)

“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. (2014)

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

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.” Men, Han, Ngoc C. Nguyen, Robert M. Freund and Jaime Peraire, MIT Sloan Working Paper. MIT Sloan School of Management, April 2013.

“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.

“A First-Order View of Boosting Methods: Computational Complexity and Connections to Regularization.” Robert M. Freund, Paul Grigas and Rahul Mazumder. In International Workshop on Advances in Regularization, Optimization, Kernel Methods and Support Vector Machines: Theory and Applications, edited by Johan Suykens, Andreas Argyriou, Kris De Brabanter, Moritz Diehl, Kristiaan Pelckmans, Marco Signoretto, Vanya Van Belle and Joos Vandewalle. Leuven, Belgium: July 2013.

“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. (2013)

“Binary optimization techniques for linear PDE-governed material design.” Saa-Seoane, Joel, Ngoc C. Nguyen, Han Men, Robert M. Freund and Jaime Peraire. Journal of Applied Physics A Vol. 109, No. 4 (2012): 1023-1030. (2012)

A Binary Optimization Method for Linear Metamaterial Design Optimization.” Joel Saa-Seoane, Ngoc C. Nguyen, Han Men, Robert M. Freund and Jaime Peraire. At 3rd International Conference on Metamaterials, Photonic Crystals and Plasmonics. Paris, France: April 2012. 

“Design of Photonic Crystals with Multiple and Combined Band Gaps.” Men, H., N.C. Nguyen, Robert M. Freund, K.M. Lim, P. Parrilo and J. Peraire. Physical Review E Vol. 85, No. 4 (2012). (2012)

“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. (2010)

“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. (2009)

“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. (2009)

“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. (2009)

“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. (2009)

“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. (2008)

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

“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. (2008)

“An Efficient Re-Scaled Perceptron Algorithm for Conic Systems.” Alexandre Belloni, Robert M. Freund and Santosh Vempala. Learning Theory: 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA, June 13-15, 2007, Proceedings (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence), edited by Nader Bshouty and Claudio Gentile. Berlin, Germany: July 2007. 

“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. (2007)

“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. (2006)

“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. (2006)

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. (2005)

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

"Data, Models, and Decisions: The Fundamentals of Management Science." Bertsimas, Dimitris and Robert Freund. Belmont, MA: Dynamic Ideas, LLC, 2004.

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

“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. (2004)

“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. (2003)

“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. (2003)

“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. (2003)

“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. (2002)

"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. (2001)

“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. (2000)

“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.

“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. (1999)

“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. (1999)

“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. (1998)

“An Improved Training Algorithm for Support Vector Machines.” Edgar Osuna, Robert M. Freund and Federico Girosi. In Nueral 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.

“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 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. (1996)

“Preface.” Anstreicher, Kurt M. and Robert M. Freund. Annals of Operations Research Vol. 62, No. 1 (1996): IX-XI. (1996)

“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. (1996)

“Interior Point Methods: Current Status and Future Directions.” Freund, Robert M. and Shinji Mizuno. Optima Vol. 51 (1996): 1-9. (1996)

“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. (1995)

“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. (1995)

“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. (1993)

“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. (1992)

“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. (1991)

“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. (1991)

“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. (1991)

“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. (1991)

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

“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. (1989)

“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. (1988)

“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. (1987)

“Economic Analysis of Product Flexible Manufacturing System Investment Decisions.” Charles H. Fine and Robert M. Freund. In Proceedings of the Second ORSA/TIMS Conference on Flexible Manufacturing Systems, edited by Kathryn Stecke and Rajan Suri. Amsterdam, Netherlands: October 1986.

“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. (1986)

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. (1985)

"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 R.W. Cottle, 1-13. Amsterdam, Netherlands: North Holland Publishing Company, 1985.  

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

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. (1984)

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

“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. (1981)

 

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Research Center(s)

General Expertise
Algorithms; Algorithms; Algorithms; Analytics; Applied math; Artificial intelligence; Big data; Computational complexity; Data analysis; Data analytics; Data mining; Data mining; Machine learning; Mathematical programming; Mathematical programming; Mathematical programming; Nonlinear optimization; Operations research; Optimization; Predictive analytics; Robust optimization