Decomposition-Invariant Pairwise Frank-Wolfe Algorithm for Constrained Multiobjective Optimization

TL;DR

This paper introduces a decomposition-invariant pairwise Frank-Wolfe algorithm for constrained multiobjective optimization, achieving linear convergence over arbitrary polytopes under strong convexity, expanding applicability beyond finite-generated polytopes.

Contribution

It presents a novel decomposition-invariant pairwise Frank-Wolfe algorithm with proven linear convergence for arbitrary bounded polytopes in multiobjective optimization.

Findings

Achieves linear convergence rate under strong convexity.

Applicable to arbitrary bounded polytopes, not just finite point sets.

Proven convergence of the entire sequence to Pareto optimal solutions.

Abstract

Recently the away-step Frank-Wolfe algoritm for constrained multiobjective optimization has been shown linear convergence rate over a polytope which is generated by finite points set. In this paper we design a decomposition-invariant pairwise frank-wolfe algorithm for multiobjective optimization that the feasible region is an arbitrary bounded polytope. We prove it has linear convergence rate of the whole sequence to a pareto optimal solution under strongly convexity without other assumptions.