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We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…

Optimization and Control · Mathematics 2024-02-12 Nguyen Anh Minh , Le Dung Muu , Tran Ngoc Thang

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Optimization and Control · Mathematics 2025-07-22 Raghu Bollapragada , Shagun Gupta

This paper studies the behavior of the extragradient algorithm [Korpelevich, 1976] when applied to hypomonotone operators, a class of problems that extends beyond the classical monotone setting. To support the understanding of this…

Optimization and Control · Mathematics 2025-01-20 Khaled Alomar , Tatjana Chavdarova

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

This paper studies proximal gradient iterations for solving simple bilevel optimization problems where both the upper and the lower level cost functions are split as the sum of differentiable and (possibly nonsmooth) proximable functions.…

Optimization and Control · Mathematics 2024-03-05 Puya Latafat , Andreas Themelis , Silvia Villa , Panagiotis Patrinos

We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued function. The proximal gradient method is probably the most…

Optimization and Control · Mathematics 2024-11-20 Christian Kanzow , Leo Lehmann

In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…

Optimization and Control · Mathematics 2023-06-29 Luis M. Briceno-Arias , Francisco José Silva , Xianjin Yang

In this work, we propose two derivative-free methods to address the problem of large-scale nonlinear equations with convex constraints. These algorithms satisfy the sufficient descent condition. The search directions can be considered…

Numerical Analysis · Mathematics 2025-11-17 Kabenge Hamiss , Mohammed M. Alshahrani , Mujahid N. Syed

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…

Optimization and Control · Mathematics 2024-12-18 Farhana A. Simi , Matthew K. Tam

We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact…

Optimization and Control · Mathematics 2020-01-06 Weijian Li , Xianlin Zeng , Shu Liang , Yiguang Hong

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…

Optimization and Control · Mathematics 2024-06-24 Morteza Maleknia , Majid Soleimani-damaneh

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…

Optimization and Control · Mathematics 2015-01-30 Yu. V. Malitsky , V. V. Semenov

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Machine Learning · Computer Science 2023-08-22 Siyuan Xu , Minghui Zhu

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

Optimization and Control · Mathematics 2021-02-18 Nguyen Van Dung , Bang Cong Vu

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to a vector subspace, a maximally monotone, a monotone-Lipschitzian, and a cocoercive…

Optimization and Control · Mathematics 2022-02-08 Luis M. Briceño-Arias , Jinjian Chen , Fernando Roldán , Yuchao Tang

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Optimization and Control · Mathematics 2016-05-02 Masoud Ahookhosh

We introduce two derivative-free projection methods for large-scale systems of nonlinear monotone equations subject to convex constraints. Both methods incorporate an adaptive spectral parameter into established conjugate gradient…

Optimization and Control · Mathematics 2026-05-18 Kabenge Hamiss , Mohammed Alshahrani , Mujahid N. Syed

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…

Optimization and Control · Mathematics 2019-01-08 Hong-Kun Xu , Vera Roshchina