On the convergence of steepest descent methods for multiobjective optimization
In this paper we consider the classical unconstrained nonlinear multiobjective optimization problem. For such a problem, it is particularly interesting to compute as many points as possible in an effort to approximate the so-called Pareto front. Consequently, to solve the problem we define an “a posteriori” algorithm whose generic iterate is represented by a set of points rather than by a single one. The proposed algorithm takes advantage of a linesearch with extrapolation along steepest descent directions with respect to (possibly not all of) the objective functions.