A Nonmonotone Front Descent Method for Bound-Constrained Multi-Objective Optimization

Abstract: We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the first descent algorithm employing nonmonotone strategies to generate point sets approximating the Pareto front. We establish convergence properties for the resulting sequences of sets, analogous to the original framework, and present numerical results confirming the approach's consistency in the bound-constrained setting.