Quasi-Newton’s method for multiobjective optimization

Abstract

In this paper we present a quasi-Newton’s method for unconstrained multiobjective optimization of strongly convex objective functions. Hence, we can approximate the Hessian matrices by using the well known BFGS method. The approximation of the Hessian matrices is usually faster than their exact evaluation, as used in, e.g., recently proposed Newton’s method for multiobjective optimization. We propose and analyze a new algorithm and prove that its convergence is superlinear.