Robert Freund

Theresa Seley Professor of Management Science
Professor of Operations Research

Biography | Selected Publications

A Geometric Analysis of Renegar’s Condition Number, and its Interplay with Conic Curvature (2009)

An Efficient Re-Scaled Perceptron Algorithm for Conic Systems (2009)

Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model (2009)

Projective Re-Normalization for Improving the Behavior of a Homogeneous Conic Linear System (2009)

On the Second-Order Feasibility Cone: Primal-Dual Representation and Efficient Projection (2008)

On the Symmetry Function of a Convex Set (2008)

Optimizing Product Line Designs: Efficient Methods and Comparisons (2008)

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

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)

Data, Models, and Decisions: The Fundamentals of Management Science (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)

 

Contact Information
Office: E62-567
Tel: (617) 253-8997
Fax: (617) 258-7579
Support Staff
Name: David V Merrill
Tel: (617) 253-3341
E-mail: dvm@mit.edu

Research Center(s)

General Expertise
Data mining; Decision making, decision support; Market research; Mathematical programming; Operations research; Optimization; Positioning; Revenue management; Singapore; Sustainability