Related papers: Strong duality and sensitivity analysis in semi-in…
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…
This paper deals with supervised classification and feature selection in high dimensional space. A classical approach is to project data on a low dimensional space and classify by minimizing an appropriate quadratic cost. A strict control…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while…
Low rank matrix recovery problems appear widely in statistics, combinatorics, and imaging. One celebrated method for solving these problems is to formulate and solve a semidefinite program (SDP). It is often known that the exact solution to…
Reinforcement learning (RL) is attracting attention as an effective way to solve sequential optimization problems that involve high dimensional state/action space and stochastic uncertainties. Many such problems involve constraints…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
Deep learning has achieved state-of-the-art performance on several computer vision tasks and domains. Nevertheless, it still has a high computational cost and demands a significant amount of parameters. Such requirements hinder the use in…
In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…
We consider semidefinite programs (SDPs) with equality constraints. The variable to be optimized is a positive semidefinite matrix $X$ of size $n$. Following the Burer--Monteiro approach, we optimize a factor $Y$ of size $n \times p$…
Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem…
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…
Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in…
We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…
Market-based mechanisms such as auctions are being studied as an appropriate means for resource allocation in distributed and mulitagent decision problems. When agents value resources in combination rather than in isolation, they must often…
We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…
We study the Constrained Convex Markov Decision Process (MDP), where the goal is to minimize a convex functional of the visitation measure, subject to a convex constraint. Designing algorithms for a constrained convex MDP faces several…
This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most…
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…