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.

  • Total dual dyadicness and dyadic generating sets (with A. Abdi, G. Cornuéjols and B. Guenin), November 2021 2111.05749.pdf

  • Clean clutters and dyadic fractional packings (with A. Abdi, G. Cornuéjols and B. Guenin), SIAM Journal on Discrete Math. , to appear dyadic.pdf

  • Matchings, hypergraphs, association schemes, and semidefinite optimization (with Y. H. (Gary) Au and N. Lindzey), August 2020 arXiv:2008.08628.pdf

  • Domain-Driven Solver (DDS): a MATLAB based software package for convex optimization problems in domain-driven form (with M. Karimi), August 2019 (revised: November 2020) arXiv:1908.03075.pdf , software

  • 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), Linear Algebra and its Applications 608 (2021) 343-362 arXiv:1805.09737.pdf The final publication is available at DOI

  • Primal-dual interior-point methods for domain-driven formulations (with M. Karimi), Mathematics of Operations Research 45 (2020) 591-621 arXiv:1804.06925.pdf The final publication is available at DOI

  • A notion of total dual integrality for convex, semidefinite, and extended formulations, (with M. K. de Carli Silva), SIAM Journal on Discrete Math. 34 (2020) 470-496 arXiv:1801.09155.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), Information Processing Letters 159-160 (2020) article 105959 arXiv:1505.01005.pdf

  • Strict complementarity in semidefinite optimization with elliptopes including the MaxCut SDP (with M. K. de Carli Silva), SIAM Journal on Optimization 29 (2019) 2650-2676 arXiv:1806.01173.pdf The final publication is available at DOI

  • Facially dual complete (nice) cones and lexicographic tangents (with V. Roshchina), SIAM Journal on Optimization 29 (2019) 2363-2387 arXiv:1704.06368.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

  • 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

  • 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

  • Polynomial optimization with a focus on hyperbolic polynomials Oberwolfach Reports OWR-2017-14 (2017) 797-800 OWR-2017-14.pdf

  • 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