A nonmonotone front descent method for bound-constrained multi-objective optimization

Abstract This paper introduces a nonmonotone extension of the Front Descent method, a state-of-the-art descent-based algorithmic framework designed to approximate the Pareto front of smooth multiobjective optimization problems. The proposed approach incorporates novel nonmonotone line search strategies that allow temporary increases in some objective functions, potentially accelerating convergence and improving overall efficiency. The theoretical analysis demonstrates that the sequence of sets generated by the algorithm retains the convergence properties of the original framework. Establishing these properties in the nonmonotone setting is nontrivial: the loss of monotonicity across the set sequence introduces substantial analytical challenges, necessitating a careful and rigorous adaptation of the original convergence arguments. Finally, numerical results in the bound-constrained setting are presented to validate the goodness of the proposed approach.