Related papers: Proximal minimization in CAT$(\kappa)$ spaces

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

This paper introduces the concept of quasi $\alpha$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $\alpha$-firmly nonexpansive mappings satisfying a…

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…

A new framework for analyzing Fejer convergent algorithms is presented. Using this framework we define a very general class of Fejer convergent algorithms and establish its convergence properties. We also introduce a new definition of…

This paper concerns a class of DC composite optimization problems which, as an extension of convex composite optimization problems and DC programs with nonsmooth components, often arises in robust factorization models of low-rank matrix…

In this paper, we introduce two novel parallel projection methods for finding a solution of a system of variational inequalities which is also a common fixed point of a family of (asymptotically) $\kappa$ - strict pseudocontractive…

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, for the problem of minimizing a class of convex objective…

We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…

In this short note, we obtain partial quasi-metric versions of Kannan's fixed point theorem for self-mappings. Moreover, we use these fixed points results to characterize a certain type of completeness in partial quasi-metric spaces. We…

We compute, using techniques originally introduced by Kohlenbach, the first author and Nicolae, uniform rates of metastability for the proximal point algorithm in the context of CAT(0) spaces (as first considered by Bacak), specifically for…

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…

In this paper, we propose a proximal splitting methodology with a non-convex penalty function based on the heavy-tailed Cauchy distribution. We first suggest a closed-form expression for calculating the proximal operator of the Cauchy…

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…

Robust learning aims to maintain model performance under noise, corruption, and distributional shifts, which are prevalent in modern machine learning applications. This work shows that examples of robust learning problems can be formulated…

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…