Publications (in reverse chronological order)

[] “Bandwidth optimization of single-polarization single-mode photonic crystal fibers,” with N.-C. Nguyen, H. Men, and J. Peraire, submitted to Optics Express.

[] “Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design,” with J. Saa-Seoane, N.-C. Nguyen, H. Men, and J. Peraire, submitted to Operations Research.

[] “A Binary Optimization Method for for Linear PDE-governed Material Design,” with J. Saa-Seoane, N.-C. Nguyen, H. Men, and J. Peraire, to appear in Journal of Applied Physics A.

[] “An Accelerated First-Order Method for Solving Unconstrained SOS Polynomial Optimization Problems,” with Dimitris Bertsimas and Xu Andy Sun, to appear in Optimization Methods and Software.

[] “Design of Photonic Crystals with Multiple and Combined Band Gaps,” with H. Men, N.C. Nguyen, 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,” with H. Men, N.C. Nguyen, P. Parrilo, and J. Peraire, Journal of Computational Physics 229 (10), pp. 3706–3725, 2010.

[] “Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model,” with Jorge Vera, Mathematics of Operations Research. 34 (4), pp. 869-879, 2009.

[] “A Geometric Analysis of Renegar’s Condition Number, and its Interplay with Conic Curvature,” with Alexandre Belloni, Mathematical Programming 119, pp. 95-107, 2009.

[] “On the Second-Order Feasibility Cone: Primal-Dual Representation and Efficient Projection,” with Alexandre Belloni, SIAM Journal on Optimization 19 (3) pp. 1073-1092, 2008.

[] “An Efficient Re-Scaled Perceptron Algorithm for Conic Systems,” with Alexandre Belloni and Santosh Vempala, Mathematics of Operations Research. 34 (3) pp. 621-641, 2009.

[] “Projective Re-Normalization for Improving the Behavior of a Homogeneous Conic Linear System,” Mathematical Programming 118, pp. 279–299, 2009.

[] “Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems,” with Fernando Ordóñez and Kim Chuan Toh, Mathematical Programming. 109 (vol.2-3), pp. 445-475, 2007.

[] “Optimizing Product Line Designs: Efficient Methods and Comparisons,” with Alexandre Belloni, Matthew Selove, and Duncan Simester, Management Science (54) 9, pp. 1544-1552, 2008.

[] “On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization,” Mathematical Programming. 106, pp. 527-545, 2006.

[] “On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems,” with Zhi Cai, Computational Optimization and Applications (34) 3, pp. 299-320, 2006.

[] “On the Symmetry Function of a Convex Set,” formerly titled “Symmetry Points of Convex Set: Basic Properties and Computational Complexity,” with Alexandre Belloni, Mathematical Programming (111), pp. 57-93, 2008.

[] “On an Extension of Condition Number Theory to Non-Conic Convex Optimization,” with Fernando Ordóñez, Mathematics of Operations Research. 30 (1), pp. 173-194, 2005.

[] “Computation of Minimum Volume Covering Ellipsoids,” with Sun Peng, Operations Research 52 (5), pp. 690-706, 2004.

[] “Computational Experience and the Explanatory Value of Condition Measures for Linear Optimization,” SIAM Journal on Optimization 14 (2), pp. 307-333, 2004.

[] "Solution Methodologies for the Smallest Enclosing Circle Problem," with Sheng Xu and Jie Sun, Computational Optimization and Applications 25, pp. 283-292, 2003.

[] “Complexity of Convex Optimization using Geometry-based Measures and a Reference Point," Mathematical Programming (99), pp. 197-221, 2004.

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

[] “A new condition measure, pre-conditioners, and relations between different measures of conditioning for conic linear systems” (formerly titled “Pre-conditioners and relations between different measures of conditioning for conic linear systems”), with Marina Epelman, SIAM Journal on Optimization 12 (3), pp. 627-655, 2002.

[] "On the Complexity of Computing Estimates of Condition Measures of a Conic Linear System," with Jorge Vera, Mathematics of Operations Research 28 (4), pp. 625-648, 2003.

[] "Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definite Program," with Manuel Nunez, SIAM Journal on Optimization 11 (3), pp. 818-836, 2001.

[] "Condition-Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm," with Jorge Vera, SIAM Journal on Optimization 10 (1), pp.155-176, 2000.

[] "Condition Number Complexity of an Elementary Algorithm for Computing a Reliable Solution of a Conic Linear System," with Marina Epelman, Mathematical Programming 88 (3), pp. 451-485, 2000.

[] "Condition Number Complexity of an Elementary Algorithm for Resolving a Conic Linear System," with Marina Epelman, MIT O.R. Working Paper 319-97, 1997.

[] "Interior Point Methods: Current Status and Future Directions," with Shinji Mizuno, in High Performance Optimization, H. Frenk et al. (eds.), Kluwer Academic Publishers, pp. 441-466, 2000.

[] "Condition Measures and Properties of the Central Trajectory of a Linear Program," with Manuel A. Nunez, Mathematical Programming 83 (1), pp. 1-28, 1998.

[] "Some Characterizations and Properties of the 'Distance to Ill-Posedness' and the Condition Measure of a Conic Linear Systems," with Jorge. R. Vera, Mathematical Programming 86, pp. 225-260, 1999.

[] "Training Support Vector Machines: an Application to Face Detection," with Edgar Osuna and Federico Girosi, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Puerto Rico, June, 1997.

[] "An Improved Training Algorithm for Support Vector Machines, " with Edgar Osuna and Federico Girosi, in Proceedings of IEEE NNSP'97, Amelia Island, Florida, September, 1997.

[] "Complexity of an Algorithm for Finding an Approximate Solution of a Semi-Definite Program, with no Regularity Condition, " O.R. Center Working Paper 302-94, December, 1994.

[] “An Infeasible-Start Algorithm for Linear Programming whose Complexity Depends on the Distance from the Starting Point to the Optimal Solution,” Annals of Operations Research 62, pp. 29-58, 1996.

[] “Following a "Balanced" Trajectory from an Infeasible Point to an Optimal Linear Programming Solution with a Polynomial-time Algorithm,” 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," with Michael J. Todd , Mathematics of Operations Research (20) 2, 415-440, 1995.

[] "A Potential Reduction Algorithm with user-specified Phase I - Phase II Balance, for Solving a Linear Program from an Infeasible Warm Start," SIAM Journal of Optimization (5) 2, 247-268, 1995.

[] "Prior Reduced Fill-In in Solving Equations in Interior-Point Algorithms", with John Birge and Robert Vanderbei , Operations Research Letters (11), pp. 195-198, 1992.

[] "Implementation and Empirical Study of a Combined Phase I - Phase II Potential Reduction Algorithm for Linear Programming," with Hitendra Wadhwa, Sloan School Working Paper #3411-92-MSA, March 1992.

[] "A Potential Function Reduction Algorithm for Solving a Linear Program Directly from an Infeasible "Warm Start"", Mathematical Programming (52) , pp. 441-466, 1991.

[] "Projective Transformation for Interior-Point Algorithms, and a Superlinearly Convergent Algorithm for the W-Center Problem," Mathematical Programming 58, pp. 385-414, 1993.

[] "A Method for the Parametric Center Problem, with a Strictly Monotone Polynomial-Time Algorithm for Linear Programming", with K. C. Tan, Mathematics of Operations Research (16), pp. 775 - 801, 1991.

[] "Theoretical Efficiency of a Shifted Barrier Function Algorithm for Linear Programming", Linear Algebra and its Applications (152), pp. 19-41 , 1991.

[] “Polynomial-time Algorithms for linear programming based only primal scaling and projected gradients of a potential function,” Mathematical Programming 51, pp. 203-222, 1991.

[] "Projective Transformations for Interior Point Methods, Part II: Analysis of An Algorithm for finding the Weighted Center of a Polyhedral System", O.R. Working Paper 18088, June 1988.

[] "Projective Transformations for In;Projective Transformations for Interior Point Methods, Part II: Analysis of An Algorithm for finding the Weighted Center of a Polyhedral System", O.R. Working Paper 18088, June 1988.

[] "Projective Transformations for Interior Point Methods, Part I: Basic Theory and Linear Programming", O.R. Working Paper 17988, June 1988.

[] "Optimal Investment in Product Flexible Manufacturing Capacity",with C. Fine, Management Science (36), pp. 449-466, 1990.

[] "Combinatorial Analogs of Brouwer's Fixed Point Theorem on a Bounded Polyhedron," Journal of Combinatorial Theory , Series B (47), pp. 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," Operations Research Letters (7), pp. 9-14, 1988.

[] "Identifying the Set of Always-Active Constraints in a System of Linear Inequalities by a Single Linear Program," with R. Roundy and M.J. Todd , Sloan School Working Paper # 1674-85, 1985.

[] "Dual Gauge Programs, with Applications to Quadratic Programming and the Minimum Norm Problem", Mathematical Programming (38), pp.47-68, 1987.

[] "Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube", Mathematics of Operations Research (11), pp. 169-179, 1986.

[] “Postoptimal Analysis of a Linear Program under Simultaneous Changes in Matrix Coefficients,”Mathematical Programming Study 24, pp. 1-13, 1985.

[] "On the Complexity of Four Polyhedral Set Containment Problems", with James B. Orlin, Mathematical Programming (33), pp.133-145, 1985.

[] "Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology", Mathematics of Operations Research (9), pp. 498-509, 1984.

[] "Variable Dimension Complexes, Part I: Basic Theory", Mathematics of Operations Research (9), pp. 479-497, 1984.

[] "Optimal Scaling of Balls and Polyhedra," with B.C. Eaves , Mathematical Programming (230) 2, pp. 138-147, 1982.

[] "A Constructive Proof of Tucker's Combinatorial Lemma," with Michael J. Todd , Journal of Combinatorial Theory (30) 2, pp. 321 -325, 1981.