12 papers · 1 filter
Second-order Methods for Multiobjective Composite Optimization: Preconditioning Strategies, Subspace Variants and Inexact Solutions
Jian Chen, Xinmin Yang
Multiobjective composite optimization problems arise in sparse regularization, constrained multiobjective models, and multi-task learning, but their numerical solution remains chal…
Preconditioned Proximal Gradient Methods with Conjugate Momentum: A Subspace Perspective
Jian Chen, Xinmin Yang
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored t…
Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization
Chengzhi Huang, Jian Chen, Liping Tang
This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Li…
Scaled Proximal Gradient Methods for Multiobjective Optimization: Improved Linear Convergence and Nesterov's Acceleration
Jian Chen, 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 ev…
First-order Methods for Unconstrained Vector Optimization Problems: A Unified Majorization-Minimization Perspective
Jian Chen, Jingjie Liu, Liping Tang +1
In this paper, we develop a unified majorization-minimization scheme and convergence analysis with first-order surrogate functions for unconstrained vector optimization problems (V…
A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems
Jian Chen, Liping Tang. Xinmin Yang
Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in con…
Barzilai-Borwein Descent Methods for Multiobjective Optimization Problems with Variable Trade-off Metrics
Jian Chen, Liping Tang, Xinmin Yang
The imbalances and conditioning of the objective functions influence the performance of first-order methods for multiobjective optimization problems (MOPs). The latter is related t…
On the Convergence of Newton-type Proximal Gradient Method for Multiobjective Optimization Problems
Jian Chen, Xiaoxue Jiang, Liping Tang +1
In a recent study, Ansary (Optim Methods Softw 38(3):570-590,2023) proposed a Newton-type proximal gradient method for nonlinear multiobjective optimization problems (NPGMO). Howev…
Barzilai-Borwein Proximal Gradient Methods for Multiobjective Composite Optimization Problems with Improved Linear Convergence
Jian Chen, Liping Tang, Xinmin Yang
When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence…
Variable Metric Method for Unconstrained Multiobjective Optimization Problems
Jian Chen, Gaoxi Li, Xinmin Yang
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive…
Convergence rates analysis of Interior Bregman Gradient Method for Vector Optimization Problems
Jian Chen, Liping Tang, Xinmin Yang
In recent years, by using Bregman distance, the Lipschitz gradient continuity and strong convexity were lifted and replaced by relative smoothness and relative strong convexity. Un…
A Barzilai-Borwein Descent Method for Multiobjective Optimization Problems
Jian Chen, Liping Tang, Xinmin Yang
The steepest descent method proposed by Fliege et al. motivates the research on descent methods for multiobjective optimization, which has received increasing attention in recent y…