Theresa Seley Professor of Management Science

Professor of Operations Research

Biography
| **Selected Publications**

“Robust topology optimization of three-dimensional photonic-crystal band-gap structures.” H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, *Optics Express *22 (19): 22632-22648, September 2014.

“Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design." Han Men, 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.” Dimitris Bertsimas, Robert M. Freund, and Xu Andy Sun. *Optimization Methods and Software *28(3): 424-441 (2013)

“Binary optimization techniques for linear PDE-governed material design.” J. Saa-Seoane, N.-C. Nguyen, H. Men, R. Freund, and J. Peraire. *Journal of Applied Physics A*. (2012)

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

“Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods." H. Men, N.C. Nguyen, R.M. Freund, P. Parrilo, and J. Peraire, *Journal of Computational Physics* 229 (10): 3706–3725 (2010)

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

“An Efficient Re-Scaled Perceptron Algorithm for Conic Systems.” Alexandre Belloni, 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.” Robert M. Freund 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.” Alexandre Belloni and Robert M. Freund. *Mathematical Programming* 118: 279-299 (2009)

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

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

“On the Symmetry Function of a Convex Set.” Alexandre Belloni and Robert M. Freund. *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.” Robert M. Freund, Fernando Ordóñez, and Kim Chuan Toh. *Mathematical Programming* 109 (vol. 2-3): 445-475 (2007)

On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization (2006)

On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems (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 (2005)

Complexity of Convex Optimization using Geometry-Based Measures and a Reference Point (2004)

Computation of Minimum Volume Covering Ellipsoids (2004)

Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization (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 (2004)

On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization (2003)

Solution Methodologies for the Smallest Enclosing Circle Problem (2003)

A new condition measure, pre-conditioners, and relations between different measures of conditioning for conic linear systems (2002)

Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi- Definite Program (2001)

Condition Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm (2000)

Condition Number Complexity of an Elementary Algorithm for Computing a Reliable Solution of a Conic Linear System (2000)

Interior Point Methods: Current Status and Future Directions, in "High Performance Optimization (2000)

Some Characterizations and Properties of the ‘Distance to Ill-Posedness’ and the Condition Measure of a Conic Linear Systems (1999)

Condition Measures and Properties of the Central Trajectory of a Linear Program (1998)

An Infeasible-Start Algorithm for Linear Programming whose Complexity Depends on the Distance from the Starting Point to the Optimal Solution (1996)

Following a “Balanced" Trajectory from an Infeasible Point to an Optimal Linear Programming Solution with a Polynomial-time Algorithm (1996)

A Potential Reduction Algorithm with user-specified Phase I - Phase II Balance, for Solving a Linear Program from an Infeasible Warm Start (1995)

Barrier Functions and Interior-Point Algorithms for Linear Programming with Zero, One-, or Two-Sided Bounds on the Variables (1995)

Projective Transformation for Interior-Point Algorithms, and a Superlinearly Convergent Algorithm for the W-Center Problem (1993)

Prior Reduced Fill-In in Solving Equations in Interior-Point Algorithms (1992)

A Method for the Parametric Center Problem, with a Strictly Monotone Polynomial-Time Algorithm for Linear Programming (1991)

A Potential Function Reduction Algorithm for Solving a Linear Program Directly from an Infeasible “Warm Start" (1991)

Polynomial-Time Algorithms for Linear Programming based only on Primal Scaling and Projected Gradients of a Potential Function (1991)

Theoretical Efficiency of a Shifted Barrier Function Algorithm for Linear Programming (1991)

Optimal Investment in Product Flexible Manufacturing Capacity (1990)

Combinatorial Analogs of Brouwer’s Fixed Point Theorem on a Bounded Polyhedron (1989)

An Analog of Karmarkar’s Algorithm for Inequality Constrained Linear Programs, with a “New” Class of Projective Transformations for Centering a Polytope (1988)

Dual Gauge Programs, with Applications to Quadratic Programming and the Minimum Norm Problem (1987)

Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube (1986)

On the Complexity of Four Polyhedral Set Containment Problems (1985)

Postoptimal Analysis of a Linear Program under Simultaneous Changes in Matrix Coefficients (1985)

Variable Dimension Complexes, Part I: Basic Theory (1984)

Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology (1984)

Optimal Scaling of Balls and Polyhedra (1982)

A Constructive Proof of Tucker's Combinatorial Lemma (1981)

**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