Robert Freund

Theresa Seley Professor of Management Science
Professor of Operations Research

Biography | Selected Publications

“New Analysis and Results for the Frank-Wolfe Method,” (formerly titled “New Analysis and Results for the Conditional Gradient Method”). Freund, Robert M., and Paul Grigas, to appear in Mathematical Programming.

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 (September 2014). Optics Express 22 (19): 22632-22648

Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design." Men, Han, Robert M. Freund, Ngoc C. Nguyen, Joel Saa-Seoane, Jaime Peraire. Operations Research, 62(2): 418-434 (2014)

An Accelerated First-Order Method for Solving Unconstrained SOS Polynomial Optimization Problems.” Bertsimas, Dimitris, Robert M. Freund, and Xu Andy Sun (2013). Optimization Methods and Software, 28(3): 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. (2012)

Design of Photonic Crystals with Multiple and Combined Band Gaps.” Men, H., N.C. Nguyen, R.M. Freund, K.M. Lim, P. Parrilo, and J. Peraire (2011). Physical Review E, 83(4). (2011)

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 (2010). Journal of Computational Physics 229(10): 3706–3725 (2010)

A Geometric Analysis of Renegar's Condition Number, and its Interplay with Conic Curvature.” Belloni, Alexandre, and Robert M. Freund (June 2009). Mathematical Programming, 119(1): 95-107

An Efficient Re-Scaled Perceptron Algorithm for Conic Systems.” Belloni, Alexandre, Robert M. Freund, and Santosh Vempala, Mathematics of Operations Research, 34(3): 621-641 (2009)

Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model.” Freund, Robert M., and Jorge Vera. Mathematics of Operations Research, 34(4): 869-879 (2009)

Projective Re-Normalization for Improving the Behavior of a Homogeneous Conic Linear System.” Belloni, Alexandre, and Robert M. Freund. Mathematical Programming 118(2): 279-299 (2009)

Optimizing Product Line Designs: Efficient Methods and Comparisons.” Belloni, Alexandre, Robert M. Freund, Matthew Selove, and Duncan I. Simester (2008). Management Science, 54(9): 1544-1553. (2008)

On the Second-Order Feasibility Cone: Primal-Dual Representation and Efficient Projection.” Belloni, Alexandre, and Robert M. Freund (2008). SIAM Journal on Optimization, 19(3): 1073-1092 (2008)

On the Symmetry Function of a Convex Set.” Belloni, Alexandre, and Robert M. Freund (2008). Mathematical Programming (111): 57-93. (2008)

A Geometric Analysis of Renegar’s Condition Number, and its Interplay with Conic Curvature (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 109(2-3): 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 (July 2006). Computational Optimization and Applications, 34(3): 299-320.

“On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization.” Freund, Robert M. (2006). Mathematical Programming, 106: 527-545. (2006)

Projective Pre-Conditioners for Improving the Behavior of a Homogeneous Conic Linear System (2006)

“On an Extension of Condition Number Theory to Non-conic Convex Optimization.” Freund, Robert M., and Fernando Ordóñez (February 2005). Mathematics of Operations Research, 30(1): 173-194.

“Computation of Minimum Volume Covering Ellipsoids.” Sun, Peng, and Robert M. Freund (September/October 2004). Operations Research, 52(5): 690-706.

“Complexity of Convex Optimization using Geometry-Based Measures and a Reference Point.” Freund, Robert M. (March 2004). Mathematical Programming, 99(2): 197-221.

“Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization.” Ordóñez, Fernando, and Robert M. Freund (2004). SIAM Journal on Optimization, 14(2): 307-333. (2004)

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

“On the Complexity of Computing Estimates of Condition Measures of a Conic Linear System.” Freund, Robert M., and Jorge Vera (2003). Mathematics of Operations Research, 28(4): 625-648. (2003)

“On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization.” Freund, Robert M. (2003). SIAM Journal on Optimization, 13(4): 1004-1013. (2003)

“Solution Methodologies for the Smallest Enclosing Circle Problem.” Xu, Sheng, Robert M. Freund, and Jie Sun (2003). Computational Optimization and Applications, 25(1-3): 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 (2002). SIAM Journal on Optimization, 12(3): 627-655. (2002)

"Condition-Measure Bounds on the Behavior of the Central Trajectory of a SemiDefinite Program." Nunez, Manuel, and Robert M. Freund (2001). SIAM Journal on Optimization, 11(3): 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 (September 2000). Mathematical Programming, 88(3): 451-485.

“Interior Point Methods: Current Status and Future Directions.” Freund, Robert M., and Shinji Mizuno. In Frenk, H. et al. (eds.), High Performance Optimization. Kluwer Academic Publishers, pp. 441-466, 2000.

“Condition Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm.” Freund, Robert M., and Jorge R. Vera (1999). SIAM Journal on Optimization, 10(1), 155-176. (1999)

“Some Characterizations and Properties of the ‘Distance to Ill-Posedness’ and the Condition Measure of a Conic Linear Systems.” Freund, Robert M., and Jorge R. Vera (1999). Mathematical Programming, 86: 225-260. (1999)

“Condition Measures and Properties of the Central Trajectory of a Linear Program.” Nunez, Manuel A., and Robert M. Freund (1998). Mathematical Programming, 83(1-3): 1-28. (1998)

“An Infeasible-Start Algorithm for Linear Programming whose Complexity Depends on the Distance from the Starting Point to the Optimal Solution.” Freund, Robert M. (1996). Annals of Operations Research, 62(1): 29-58. (1996)

“Following a “Balanced” Trajectory from an Infeasible Point to an Optimal Linear Programming Solution with a Polynomial-time Algorithm.” Freund, Robert M. (1996). Mathematics of Operations Research, 21(4): 839-859. (1996)

“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 (May 1995). Mathematics of Operations Research, 20(2): 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. (1995). SIAM Journal of Optimization, 5(2): 247-268. (1995)

“Projective Transformation for Interior-Point Algorithms, and a Superlinearly Convergent Algorithm for the W-Center Problem.” Freund, Robert M. (1993). Mathematical Programming, 58(1-3): 385-414. (1993)

“Prior Reduced Fill-In in Solving Equations in Interior-Point Algorithms.” Birge, John R., Robert M. Freund, and Robert Vanderbei (1992). Operations Research Letters, 11(4): 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 (November 1991). Mathematics of Operations Research, 16(4): 775-801.

“Theoretical Efficiency of a Shifted Barrier Function Algorithm for Linear Programming.” Freund, Robert M. (July 1991). Linear Algebra and its Applications, 152(1): 19-41.

“A Potential Function Reduction Algorithm for Solving a Linear Program Directly from an Infeasible 'Warm Start.'” Freund, Robert M. (1991). Mathematical Programming, 52(1-3): 441-466. (1991)

“Polynomial-Time Algorithms for Linear Programming based only on Primal Scaling and Projected Gradients of a Potential Function.” Freund, Robert M. (1991). Mathematical Programming, 51(1-3): 203-222 . (1991)

“Optimal Investment in Product Flexible Manufacturing Capacity.” Fine, Charles H., and Robert M. Freund (1990). Management Science, 36(4): 449-466. (1990)

“Combinatorial Analogs of Brouwer’s Fixed Point Theorem on a Bounded Polyhedron.” Freund, Robert M. (1989). Journal of Combinatorial Theory, Series B, 47(2): 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. (February 1988). Operations Research Letters, 7(1): 9–14.

“Dual Gauge Programs, with Applications to Quadratic Programming and the Minimum Norm Problem.” Freund, Robert M. (1987). Mathematical Programming, 38(1): 47–68. (1987)

“Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube.” Freund, Robert M. (1986). Mathematics of Operations Research, 11(1): 169-179. (1986)

“On the Complexity of Four Polyhedral Set Containment Problems.” Freund, Robert M., and James B. Orlin (1985). Mathematical Programming, 33(2): 133-145. (1985)

“Postoptimal Analysis of a Linear Program under Simultaneous Changes in Matrix Coefficients.” Freund, Robert M. (1985). Mathematical Programming Study, 24: 1-13. (1985)

“Variable Dimension Complexes, Part I: Basic Theory.” Freund, Robert M. (1984). Mathematics of Operations Research, 9(4): 479-497. (1984)

“Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology.” Freund, Robert M. (1984). Mathematics of Operations Research, 9(4): 498-509. (1984)

“Optimal Scaling of Balls and Polyhedra." Eaves, B.C., and Robert M. Freund (1982). Mathematical Programming, 23(1): 138-147. (1982)

“A Constructive Proof of Tucker’s Combinatorial Lemma.” Freund, Robert M., and Michael J. Todd (May 1981). Journal of Combinatorial Theory, 30(3): 321-325.

 

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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