A Quasi-Newton Method with Wolfe Line Search for Multiobjective Optimization

Proceedings of the 29th IME/UFG Week (PDF) | Slides (PDF)

Summary: We propose a BFGS method with Wolfe line search for unconstrained multiobjective optimization problems. The algorithm is well-defined even for general nonconvex problems. Global and R-linear convergence to a Pareto optimal point are established for strongly convex problems. In the local convergence analysis, if the objective functions are locally strongly convex with Lipschitz-continuous Hessians, then the convergence rate is Q-superlinear. In this sense, our method exactly reproduces the behavior of the classical BFGS method for scalar optimization.