My current research focuses on developing tractable relaxations and efficient algorithms with strong theoretical performance guarantees for solving challenging large scale optimization problems under uncertainty with applications in compressed sensing, high dimensional statistical inference and machine learning. In this domain, jointly with Profs. Arkadi Nemirovski and Anatoli Juditsky, I have derived verifiable sufficient conditions for sparse signal recovery, utilized these conditions in the restricted matrix design problem and analyzed first order optimization methods (with both deterministic and stochastic oracles) for solving bilinear saddle point problems in various applications.
In addition to my dissertation work, I have done research on real-time decision making and discrete optimization. I have co-authored a paper examining the effects of objective function uncertainties in binary mixed integer linear programs, specifically analyzing the stability of a solution with respect to changes in the objective function, which can be utilized in sequential real time decision making scenarios such as iterative combinatorial auctions. Moreover, in collaboration with Profs. George Nemhauser and Martin Savelsbergh, I developed a novel approach that employs restarts and exploits the information contained in fathomed subproblems to effectively reduce the risk of incurring inappropriate branchings within a branch-and-cut framework and is shown to significantly improve the performance of state of the art commercial solvers.
Furthermore production planning and scheduling has been a part of my research agenda starting from my master's degree. My masters thesis addressed issues on flexible manufacturing concerning optimal coordination of tool transportation and job sequencing. Besides, in 2007, I have done a summer internship at IBM T.J. Watson Research Lab working on complex industrial scheduling problem arising from steel manufacturing.
Overall, I have a strong interest for providing quantitative methodologies to aid decision making in complex operational settings such as inventory and supply chain management, production planning and scheduling and revenue management while taking into account dynamic and competitive nature of operations and uncertainties in data.