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 Renegarâ€™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.

**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