A superlinearly convergent nonmonotone quasi-Newton method for unconstrained multiobjective optimization. (1st November 2020) - Mahdavi-Amiri, N.; Salehi Sadaghiani, F.
ABSTRACT: We propose and analyse a nonmonotone quasi-Newton algorithm for unconstrained strongly convex multiobjective optimization. In our method, we allow for the decrease of a convex combination of recent function values. We establish the global convergence and local superlinear rate of convergence under reasonable assumptions. We implement our scheme in the context of BFGS quasi-Newton method for solving unconstrained multiobjective optimization problems. Our numerical results show that the nonmonotone quasi-Newton algorithm uses fewer function evaluations than the monotone quasi-Newton algorithm.