  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.
