Related papers: Smoothing Iterative Consensus-based Optimization A…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
In this manuscript we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the second order in time dynamics, combining viscous and Hessian-driven damping with a…
This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems. In this note we synthesize…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…
This paper considers a consensus optimization problem, where all the nodes in a network, with access to the zeroth-order information of its local objective function only, attempt to cooperatively achieve a common minimizer of the sum of…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
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 focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem potentially being nonsmooth. We develop a two-timescale…
We propose an accelerated forward-backward method with fast convergence rate for finding a minimizer of a decomposable nonsmooth convex function over a closed convex set, and name it smoothing accelerated proximal gradient (SAPG) algorithm.…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which…