Research Interests

My research program lies in the areas of mathematical optimization, mathematics of operations research and foundations of computational mathematics. The focus of the program is on commonly encountered optimization problems (including linear and nonlinear programming and combinatorial optimization problems). The research program aims at understanding the structure of some problems in the aforementioned class and provably efficient methods for solving them.

Recent Publications

The file list.html includes a list of my publications and pointers to the ps and/or pdf files of some papers. The following is a list of recent research reports.

  • Status determination by interior-point methods for convex optimization problems in domain-driven form (with M. Karimi), January 2019 arXiv:1901.007084.pdf

  • On the spectral structure of Jordan-Kronecker products of symmetric and skew-symmetric matrices (with N. Kalantarova), May 2018 arXiv:1805.09737.pdf

  • Pointed closed convex sets are the intersection of all rational supporting closed halfspaces (with M. K. de Carli Silva), February 2018 arXiv:1802.03296.pdf

  • A notion of total dual integrality for convex, semidefinite, and extended formulations, (with M. K. de Carli Silva), January 2018 arXiv:1801.09155.pdf

  • Strict complementarity in semidefinite optimization with elliptopes including the MaxCut SDP (with M. K. de Carli Silva), June 2018 (revised: February 2019) SIAM Journal on Optimization to appear arXiv:1806.01173.pdf

  • Facially dual complete (nice) cones and lexicographic tangents (with V. Roshchina), April 2017 (revised: December 2018) SIAM Journal on Optimization , to appear arXiv:1704.06368.pdf

  • Primal-dual interior-point methods for domain-driven formulations (with M. Karimi), April 2018 (revised: October 2018) Mathematics of Operations Research , to appear arXiv:1804.06925.pdf

  • Elementary polytopes with high lift-and-project ranks for strong positive semidefinite operators (with Y. H. (Gary) Au), Discrete Optimization 27 (2018) 103-129 arXiv:1608.07647.pdf The final publication is available at DOI

  • Approximation ratio of LD algorithm for multi-processor scheduling and the Coffman-Sethi conjecture (with P. S. Ravi), May 2015 (revised: October 2018) arXiv:1505.01005.pdf

  • Quantum and classical coin-flipping protocols based on bit-commitment and their point games (with A. Nayak and J. Sikora), April 2015 arXiv:1504.04217.pdf

  • Interior-point algorithms for convex optimization based on primal-dual metrics (with T. G. J. Myklebust), November 2014 (revised: April 2016) arXiv:1411.2129.pdf

  • A utility theory based interactive approach to robustness in linear optimization (with M. Karimi and S. Moazeni), Journal of Global Optimization 70 (2018) 811-842 arXiv:1312.4489.pdf The final publication is available at Springer via DOI

  • An axiomatic duality framework for the theta body and related convex corners (with M. K. de Carli Silva), Mathematical Programming A 162 (2017) 283-322 arXiv:1412.2103.pdf. The final publication is available at Springer via DOI

  • Lovász-Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs (with S. M. Bianchi, M. S. Escalante and G. L. Nasini), Mathematical Programming A 162 (2017) 201-223 arXiv:1411.2069.pdf. The final publication is available at Springer via DOI

  • Primal-dual entropy based interior-point algorithms for linear optimization (with M. Karimi and S. Luo), RAIRO Operations Research 51 (2017) 299-328 arXiv:1410.8226.pdf The final publication is available at DOI

  • Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime (with P. S. Ravi and M. Huang), Journal of Scheduling 19 (2016) 547-561 arXiv:1312.3345.pdf. The final publication is available at Springer via DOI

  • A comprehensive analysis of polyhedral lift-and-project methods (with Y. H. (Gary) Au), SIAM Journal on Discrete Math. 30 (2016) 411-451 arXiv:1312.5972.pdf

  • A search for quantum coin-flipping protocols using optimization techniques (with A. Nayak and J. Sikora), Mathematical Programming A 156 (2016) 581-613 arXiv:1403.0505.pdf, arXiv:1403.0505-supplemental-material.pdf, source codes. The final publication is available at Springer via DOI

  • Local superlinear convergence of polynomial-time interior-point methods for hyperbolicity cone optimization problems (with Yu. Nesterov), SIAM Journal on Optimization 26 (2016) 139-170 arXiv:1412.1857.pdf

  • Perturbed sums of squares theorem for polynomial optimization and its applications (with M. Muramatsu and H. Waki), Optimization Methods and Software 31 (2016) 134-156 arXiv:1304:0065.pdf.

  • Efficient heuristic algorithms for maximum utility product pricing problems (with T. G. J. Myklebust and M. A. Sharpe), Computers and Operations Research 69 (2016) 25-39 pricedown.pdf, source codes and data.

  • Vertices of spectrahedra arising from the elliptope, the theta body, and their relatives (with M. K. de Carli Silva), SIAM Journal on Optimization 25 (2015) 295-316 arXiv:1309.7415.pdf

  • On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs (with Y. Awate, G. Cornuéjols and B. Guenin), Mathematical Programming A 150 (2015) 459-489 relative-strength-intersection-cuts.pdf. The final publication is available at Springer via DOI

  • Applications of deterministic optimization techniques to some probabilistic choice models for product pricing using reservation prices (with R. Shioda and B. Hui), Pacific Journal of Optimization 10 (2014) 767-808 LongVersionShioda-Tuncel-Hui.pdf.

  • Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope (with S. M. Bianchi, M. S. Escalante and G. L. Nasini), Discrete Appl. Math. 164 (2014) 460-469 BENT_DAM.pdf

  • Lovász-Schrijver SDP-operator and a superclass of near-perfect graphs (with S. M. Bianchi, M. S. Escalante and G. L. Nasini), Electronic Notes on Discrete Mathematics 44 (2013) 339-344.

  • Optimization problems over unit distance representations of graphs (with M. K. de Carli Silva), Electronic Journal of Combinatorics 20 (2013) #P43 arXiv:1010.6036.pdf errata.pdf

  • S-goodness for low-rank matrix recovery (with L. Kong and N. Xiu), Abstract and Applied Analysis 2013 (2013) arXiv:1106.3276.pdf

  • Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems (with L. Kong and N. Xiu), Mathematical Programming A 133 (2012) 327-336 corr2007-07.pdf. The final publication is available at Springer via DOI

  • Existence and uniqueness of solutions for homogeneous cone complementarity problems (with L. Kong and N. Xiu), Journal of Optimization Theory and Applications 153 (2012) 357-376 arXiv:0904.1827.pdf. The final publication is available at Springer via DOI

  • Strong duality and minimal representations for cone optimization (with H. Wolkowicz), Computational Optimization and Applications 53 (2012) 619-648 corr2008-07.pdf. The final publication is available at Springer via DOI

  • Complexity Analyses of Bienstock-Zuckerberg and Lasserre Relaxations on the Matching and Stable Set Polytopes (with Y. H. (Gary) Au), Proceedings of the 15th International Conference on Integer Programming and Combinatoral Optimization (IPCO 2011) New York, NY, USA, June 15-17, 2011, Lecture Notes in Computer Science 6655, Springer 2011, pp. 14-26.

  • Equivalent conditions for Jacobian nonsingularity in linear symmetric cone programming (with L. Kong and N. Xiu), Journal of Optimization Theory and Applications 148 (2011) 364-389 corr2008-12.pdf. The final publication is available at Springer via DOI

  • Near-perfect graphs with polyhedral N_+(G) (with S. M. Bianchi, M. S. Escalante and G. L. Nasini), Electronic Notes on Discrete Mathematics 37 (2011) 393-398.

  • Some advances on Lovász-Schrijver N_+(.) relaxations on the fractional stable set polytope (with S. M. Bianchi, M. S. Escalante and G. L. Nasini), Electronic Notes on Discrete Mathematics 37 (2011) 189-194.

  • Maximum utility product pricing models and algorithms based on reservation prices (with R. Shioda and T. G. J. Myklebust), Computational Optimization and Applications 48 (2011) 157-198 journal-version.pdf. The final publication is available at Springer via DOI

  • The Fischer-Burmeister complementarity function on Euclidean Jordan algebras (with L. Kong and N. Xiu), Pacific Journal of Optimization 6 (2010) 423-440 corr2007-17.pdf.

  • Self-concordant barriers for convex approximations of structured convex sets (with A. Nemirovski), Foundations of Computational Mathematics 10 (2010) 485-525 corr2007-03.pdf, article.