Global convergence of a modified BFGS-type method based on function information for nonconvex multiobjective optimization problems

We propose a modified BFGS-type method based on function information for nonconvex multiobjective optimization problems (MFQNMO). The method employs a common BFGS matrix to approximate the Hessian matrix of all objective functions in each iteration. This matrix is updated using function and gradient information from the previous step. Our analysis confirms the convergence of the method without relying on convexity assumptions. We also establish a local superlinear convergence rate for MFQNMO under mild conditions and validate its effectiveness through experiments on both nonconvex and convex test problems.