[] “An Extended Frank-Wolfe Method with ``In-Face" Directions, and its Application to Low-Rank Matrix Completion” with Rahul Mazumder and Paul Grigas, submitted to *SIAM Journal on Optimization*.

[] “New Computational Guarantees for Solving Convex Optimization Problems with First Order Methods, via a Function Growth Condition Measure” with Haihao Lu, submitted to *Mathematical Programming*.

[] “A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives” with Paul Grigas and Rahul Mazumder, submitted to *Annals of Statistics*.

[] “Gaussian functional regression for state prediction using linear PDE models and observations,” with N. C. Nguyen, H. Men, and J. Peraire, submitted to *SIAM Journal on Scientific Computing* 2015.

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

[] “Designing Phononic Crystals with Conic Convex Optimization,” with Han Men, N.-C. Nguyen, Joel Saa-Seoane, and Jaime Peraire, ASME2013 International Mechanical Engineering Congress and Exposition, pp. V014T15A047, San Diego, November 2013.

[] “New Analysis and Results for the Frank-Wolfe Method,” (formerly titled "New Analysis and Results for the Conditional Gradient Method") with Paul Grigas, to appear in *Mathematical Programming*.

[] “AdaBoost and Forward Stagewise Regression are First-Order Convex Optimization Methods,” with Paul Grigas and Rahul Mazumder, MIT Operations Research Center working paper OR 397-14.

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

[] “Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design,” with J. Saa-Seoane, N.-C. Nguyen, H. Men, and J. Peraire, *Operations Research* 62 (2), pp. 418-434, 2014.

[] “A Binary Optimization Method for for Linear PDE-governed Material Design,” with J. Saa-Seoane, N.-C. Nguyen, H. Men, and J. Peraire, *Journal of Applied Physics A* 109 (4), pp. 1023-1030, 2012.

[] “An Accelerated First-Order Method for Solving Unconstrained
SOS Polynomial Optimization Problems,”
with Dimitris Bertsimas and Xu Andy Sun, *Optimization Methods and Software* 28 (3), pp. 424-441, 2013.

[] “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.

[] "An Analog of Karmarkar's Algorithm for Inequality Constrained Linear Programs, with a "New" Class of Projective Transformations for Centering a Polytope,"

[] "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",

[] "Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube",

[] “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.