Multiibjective optimization : an inertial dynamical approach to Pareto optima

TL;DR

This paper introduces a gradient-based inertial dynamical system for multi-objective optimization, proving solution existence and convergence to Pareto optimal points, aiming to develop faster numerical methods.

Contribution

It presents a novel second-order differential equation approach with inertial effects for multi-objective optimization, including convergence analysis.

Findings

Existence of global solution trajectories established.

Trajectories converge to weak Pareto points in convex cases.

Lays groundwork for efficient numerical algorithms.

Abstract

We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential equation, and their convergence to weak Pareto points in the convex case. It is a first step towards the design of fast numerical methods for multi-objective optimization.