相关论文: A splitting proximal point method for Nash-Cournot…

We provide a simple and flexible framework for designing differentially private algorithms to find approximate stationary points of non-convex loss functions. Our framework is based on using a private approximate risk minimizer to "warm…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…

Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver NExOS…

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

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…

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

In this paper, we present a novel consensus-based zeroth-order algorithm tailored for non-convex multiplayer games. The proposed method leverages a metaheuristic approach using concepts from swarm intelligence to reliably identify global…

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with joint feasibility constraints and expected-value cost functions. We propose a distributed stochastic projected reflected gradient algorithm and show its almost…

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we first propose a new Newton-CG method for finding an approximate…

In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

This work examines a stochastic formulation of the generalized Nash equilibrium problem (GNEP) where agents are subject to randomness in the environment of unknown statistical distribution. We focus on fully-distributed online learning by…

This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one…

We study the sensitivity of optimal solutions of convex separable optimization problems over an integral polymatroid base polytope with respect to parameters determining both the cost of each element and the polytope. Under convexity and a…

We consider the Nash equilibrium problem in a partial-decision information scenario. Specifically, each agent can only receive information from some neighbors via a communication network, while its cost function depends on the strategies of…

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…

We discuss equations associated to Cournot-Nash Equilibria as put forward recently by Blanchet and Carlier. These equations are related to an optimal transport problem in which the source measure is known, but the target measure is part of…