A Trust Region Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems

TL;DR

This paper introduces a new trust region proximal gradient method for solving nonlinear multi-objective optimization problems, ensuring convergence without requiring prior parameter tuning or objective ordering.

Contribution

It presents a globally convergent algorithm that handles composite objectives with smooth and nonsmooth parts, using a novel trust region approach and quadratic approximations.

Findings

Method is verified on benchmark problems.

Compared favorably with existing methods.

Convergence to critical points is established.

Abstract

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a sub problem is solved to find a suitable direction. This sub problem uses a quadratic approximation of each smooth function and a trust region constraint. An update formula for trust region radius is introduce in this paper. A sequence is generated using descent directions. It is justified that under some mild assumptions every accumulation point of this sequence is a critical point. The proposed method is verified and compared with some existing methods using a set of problems.