相关论文: Characterization of the norm-based robust solution…

Structured statistical estimation problems are often solved by Conditional Gradient (CG) type methods to avoid the computationally expensive projection operation. However, the existing CG type methods are not robust to data corruption. To…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…

Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…

We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

We consider the optimization of the vector of grasping forces that support a known generalized force acting on the grasped object---a rigid body or a mechanism. Working in the framework of finite-dimensional normed vector spaces and their…

We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…

In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration,…

In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is…

In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through…

We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free…