Research
My research centers on continuous optimization, with an emphasis on complexity analysis and scalable algorithms for large linear, conic, and nonlinear models. I am advised by Anton J. Kleywegt, Renato D.C. Monteiro, and Dmitrii M. Ostrovskii and I work closely with Arkadi Nemirovski, Santanu Dey, Diego Cifuentes, Vincent Guigues, Victor Hugo Nascimento, and Arnesh Sujanani.
People and Venues
Advisors and collaborators
My primary advising relationship is with Anton J. Kleywegt and Renato D.C. Monteiro. I also collaborate on recent projects with Arkadi Nemirovski, Santanu Dey, Dmitrii M. Ostrovskii, Diego Cifuentes, Vincent Guigues, Victor Hugo Nascimento, and Arnesh Sujanani.
Submission venues
Current Directions
Major direction
I develop efficient algorithms for large-scale linear programming, convex quadratic programming, semidefinite programming, complementarity problems, variational inequalities, nonlinear convex programming, and continuous relaxations of combinatorial optimization problems.
Parallel direction
I also work on fast numerical methods and software for large optimization problems, with particular interest in low-rank structure and GPU-accelerated first-order solvers.
With Santanu Dey and Renato D.C. Monteiro, I study optimization for energy systems, including alternating-current optimal power flow (AC-OPF). This research focuses on faster algorithms for solving the associated semidefinite programming (SDP) relaxations.
Selected Work
The link order is consistent across entries: paper, code, and supporting files.
Submitting to Mathematical Programming
Oracle lower bounds for randomized and parallel methods under entropy relative smoothness, including polynomial-size query batches in sufficiently large dimensions.
Submitting to Mathematical Programming Computation
Work in progress
We develop low-rank augmented Lagrangian methods for solving large-scale semidefinite relaxations of phase retrieval.
Submitted to Mathematics of Operations Research
Submitted to SIAM Journal of Optimization
An Ω(L/T) lower bound for entropy-smooth convex optimization, showing that mirror descent is optimal up to a logarithmic factor.
Submitted to Mathematical Programming Computation
GPU-accelerated low-rank methods for semidefinite programs with large, structured instances.
Submitted to Mathematical Programming
Submitted to Mathematical Programming
Sparse augmented Lagrangian and Frank-Wolfe-based methods for large-scale linear programming.
Submitted to Operations Research
Continuous optimization methods for bicriterion traffic assignment, together with large transportation benchmark instances.
Submitted to Mathematical Programming
Adaptive homotopy smoothing for bicriteria traffic assignment with general preference distributions, including atoms and gaps. Combines relaxed Frank–Wolfe iterations with computable objective-error bounds and parametric shortest-path column generation, with complexity guarantees and experiments on 17 benchmark networks.