Related papers: Proportional-Integral Projected Gradient Method fo…
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"'…
Under the strongly convex assumption, several recent works studied the global linear convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions and a…
Primal-dual hybrid gradient method (PDHG, a.k.a. Chambolle and Pock method) is a well-studied algorithm for minimax optimization problems with a bilinear interaction term. Recently, PDHG is used as the base algorithm for a new LP solver…
This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…
In this paper, we present the proximal-proximal-gradient method (PPG), a novel optimization method that is simple to implement and simple to parallelize. PPG generalizes the proximal-gradient method and ADMM and is applicable to…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…
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…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
We study convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly nonconvex) sets and when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We study projection-free methods for functional constrained optimization with convex or smooth nonconvex objectives. Such problems arise in applications such as portfolio optimization and radiation therapy planning, where risk-aware…
In this paper we develop accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient (LLCG), which is beyond the well-studied class of convex optimization with Lipschitz continuous gradient. In…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…