Multiobjective Balanced Gradient Flow: A Dynamical Perspective on a Class of Optimization Algorithms

TL;DR

This paper introduces the Multiobjective Balanced Gradient Flow (MBGF), a new dynamical system for multi-objective optimization, demonstrating convergence properties and rates for convex and non-convex problems.

Contribution

It presents a novel dynamical system framework for normalized gradient methods in multi-objective optimization, with theoretical convergence guarantees.

Findings

Solutions exist under certain assumptions.

Convergence to weak Pareto points in convex cases.

Established convergence rates for convex and non-convex scenarios.

Abstract

This paper proposes a novel dynamical system called the Multiobjective Balanced Gradient Flow (MBGF), offering a dynamical perspective for normalized gradient methods in a class of multi-objective optimization problems. Under certain assumptions, we prove the existence of solutions for MBGF trajectories and establish their convergence to weak Pareto points in the case of convex objective functions. For both convex and non-convex scenarios, we provide convergence rates of $O(1/t)$ and $O(1/\sqrt{t})$, respectively.