Métodos Quase-Newton com busca linear de Wolfe para otimização multiobjetivo

Abstract

We propose three BFGS-type methods withWolfe line search for unconstrained multiobjective optimization. The algorithms are well defined even for general nonconvex problems. The first one mimics the classical BFGS method for scalar optimization, for which global convergence and R-linear convergence to a Pareto optimal point are established for strongly convex problems. In the local convergence analysis, the rate is Q-superlinear. The other two algorithms are globally convergent versions of the BFGS method for nonconvex problems. Finally, we explicitly characterize in a non-asymptotic way the superlinear local convergence of the BFGS method for multiobjective optimization.