Related papers: Second-order Conic Programming Approach for Wasser…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
This paper addresses a novel \emph{cost-sensitive} distributionally robust log-optimal portfolio problem, where the investor faces \emph{ambiguous} return distributions, and a general convex transaction cost model is incorporated. The…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
We consider exact deterministic mixed-integer programming (MIP) reformulations of distributionally robust chance-constrained programs (DR-CCP) with random right-hand sides over Wasserstein ambiguity sets. The existing MIP formulations are…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…
In this paper, we show that the standard semidefinite programming (SDP) relaxation of altering current optimal power flow (AC OPF) can be equivalently reformulated as second-order cone programming (SOCP) relaxation with maximal clique- and…
We extend rank-constrained optimization to general hyperbolic programs (HP) using the notion of matroid rank. For LP and SDP respectively, this reduces to sparsity-constrained LP and rank-constrained SDP that are already well-studied. But…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage…
Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially…
In this paper we consider finding an approximate second-order stationary point (SOSP) of nonconvex conic optimization that minimizes a twice differentiable function over the intersection of an affine subspace and a convex cone. In…
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…