Related papers: Universal methods for variational inequalities: de…
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our…
In this paper, we consider the problems of approximating uncertainties and feedback control for a class of nonlinear systems without full-known states, and two approximation methods are proposed: universal approximation using integral-chain…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…
In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…
Stochastic methods for minimizing a convex integral functional, as initiated by Robbins and Monro in the early 1950s, rely on the evaluation of a gradient (or subgradient if the function is not smooth) and moving in the corresponding…
In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…
This paper presents a proximal-point-based catalyst scheme for simple first-order methods applied to convex minimization and convex-concave minimax problems. In particular, for smooth and (strongly)-convex minimization problems, the…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequalities (SCVI) where the set is given as the Cartesian product of a collection of component…
This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in…
We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…
We propose an adaptive proximal gradient method for minimizing the sum of two functions, where one is a simple convex function, and the other belongs to one of the three classes: nonconvex smooth, convex nonsmooth, or convex smooth. The key…
Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…