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The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein "two-point step size" strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the…

Optimization and Control · Mathematics 2016-10-13 Frank E. Curtis , Wei Guo

In this paper, we propose a new non-monotone line-search method for smooth unconstrained optimization problems with objective functions that have many non-global local minimizers. The method is based on a relaxed Armijo condition that…

Optimization and Control · Mathematics 2025-02-27 Zohreh Aminifard , Geovani Nunes Grapiglia

In this paper, we develop a unified majorization-minimization scheme and convergence analysis with first-order surrogate functions for unconstrained vector optimization problems (VOPs). By selecting different surrogate functions, the…

Optimization and Control · Mathematics 2026-01-14 Jian Chen , Jingjie Liu , Liping Tang , Xinmin Yang

Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for…

Optimization and Control · Mathematics 2024-11-13 Jian Chen , Liping Tang , Xinmin Yang

We analyze a pointwise tracking multiobjective optimal control problem subject to the Poisson problem and bilateral control constraints. To approximate Pareto optimal points and the Pareto front numerically, we consider two different finite…

Optimization and Control · Mathematics 2025-05-21 Francisco Fuica , Stefan Volkwein

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

Stochastic multi-objective optimization (SMOO) has recently emerged as a powerful framework for addressing machine learning problems with multiple objectives. The bias introduced by the nonlinearity of the subproblem solution mapping…

Optimization and Control · Mathematics 2024-10-10 Linxi Yang , Liping Tang , Jiahao Lv , Yuehong He , Xinmin Yang

In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent iterative method, is proposed and analyzed to find multiple…

Numerical Analysis · Mathematics 2024-04-16 Wei Liu , Ziqing Xie , Wenfan Yi

This paper studies optimization problems over multi-agent systems, in which all agents cooperatively minimize a global objective function expressed as a sum of local cost functions. Each agent in the systems uses only local computation and…

Optimization and Control · Mathematics 2025-05-26 Jinhui Hu , Xin Chen , Lifeng Zheng , Ling Zhang , Huaqing Li

This paper addresses the challenge of developing efficient algorithms for large-scale nonconvex multiobjective optimization problems (MOPs). While quasi-Newton methods are effective, their traditional application to MOPs is computationally…

Optimization and Control · Mathematics 2025-12-23 Hua Liu

In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…

Optimization and Control · Mathematics 2018-08-02 Sebastian Peitz , Michael Dellnitz

In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guaranteed. Under mild assumptions on the…

Numerical Analysis · Mathematics 2010-11-02 G. C. Bento , O. P. Ferreira , P. R. Oliveira

We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the…

Optimization and Control · Mathematics 2025-09-03 Pierluigi Mansueto

This paper addresses unconstrained multiobjective optimization problems where two or more continuously differentiable functions have to be minimized. We delve into the conjugate gradient methods proposed by Lucambio P\'{e}rez and Prudente…

Optimization and Control · Mathematics 2024-10-15 Wang Chen , Yong Zhao , Liping Tang , Xinmin Yang

In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoretical result regarding the computation of descent directions…

Optimization and Control · Mathematics 2021-03-05 Bennet Gebken , Sebastian Peitz

Due to simplicity, computational cheapness, and efficiency, the Barzilai and Borwein (BB) gradient method has received a significant amount of attention in different fields of optimization. In the first part of this paper, based on spectral…

Optimization and Control · Mathematics 2018-06-29 Behzad Azmi , Karl Kunisch

This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…

Optimization and Control · Mathematics 2025-02-05 Nguyen Duc Anh , Tran Ngoc Thang

In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…

Optimization and Control · Mathematics 2025-03-25 Anteneh Getachew Gebrie , Ellen Hidemi Fukuda

Variable metric proximal gradient (VM-PG) is a widely used class of convex optimization method. Lately, there has been a lot of research on the theoretical guarantees of VM-PG with different metric selections. However, most such metric…

Optimization and Control · Mathematics 2019-10-17 Youngsuk Park , Sauptik Dhar , Stephen Boyd , Mohak Shah

This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth…

Optimization and Control · Mathematics 2025-07-11 Barsha Shaw , Md Abu Talhamainuddin Ansary