相关论文: A Bregman firmly nonexpansive proximal operator fo…

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…

The paper presents primal-dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat-Vu…

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of many optimization algorithms. Firmly nonexpansive operators…

Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…

Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. Five years ago, it was shown that if finitely many firmly nonexpansive mappings have or "almost have" fixed…

We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…

Maximally monotone operators and firmly nonexpansive mappings play key roles in modern optimization and nonlinear analysis. Five years ago, it was shown that if finitely many firmly nonexpansive operators are all asymptotically regular…

We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…

We develop a new variational approach on level sets aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. With this new approach,…

The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems,…

In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving a proximal-type subproblem with an abstract Bregman distance based proximal term. We prove their convergence when…

Structured convex optimization problems typically involve a mix of smooth and nonsmooth functions. The common practice is to activate the smooth functions via their gradient and the nonsmooth ones via their proximity operator. We show that,…

Operator splitting methods have been successfully used in computational sciences, statistics, learning and vision areas to reduce complex problems into a series of simpler subproblems. However, prevalent splitting schemes are mostly…

We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…

The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We…

This note studies the distributed non-convex optimization problem with non-smooth regularization, which has wide applications in decentralized learning, estimation and control. The objective function is the sum of different local objective…

This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…