A Homotopy Framework for Constrained Multiobjective Optimization

TL;DR

This paper introduces a homotopy-based method for solving constrained multiobjective optimization problems, providing a deterministic path to Pareto solutions with demonstrated robustness and efficiency.

Contribution

It develops a novel homotopy framework that guarantees convergence to KKT points and shows competitive performance against existing methods.

Findings

Method converges globally to Pareto-stationary solutions.

Robust convergence even from nonfeasible initial points.

Competitive computational efficiency compared to classical methods.

Abstract

We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with the multiobjective problem, yielding a deterministic and structure-preserving continuation path. Under mild regularity assumptions, we establish global convergence of the homotopy trajectory to a Pareto-stationary solution for any initial point chosen in the interior of the feasible region. In numerical experiments, the method exhibits robust convergence even when initialized from nonfeasible points, indicating stability beyond the theoretical guarantees. Efficient predictor-corrector continuation strategies are employed to trace the homotopy path. Numerical results on benchmark problems compare the proposed approach with classical scalarization methods and the evolutionary algorithm NSGA-II, demonstrating competitive computational efficiency and consistent solution quality. These results highlight the effectiveness of the homotopy framework for constrained multiobjective optimization and motivate extensions to more general problem settings and adaptive parameter strategies.