On gradient-like dynamic systems for multi-objective optimization. Convergence of trajectories to Pareto optima

Abstract

In a general Hilbert framework, we consider continuous gradient-like dynamic systems for constrained multi-objective optimization, involving (possibly non-smooth) convex objective functions. We prove a descent property for each objective function, and the convergence of trajectories to weak Pareto minima. This approach provides a dynamical endogenous weighting of the criteria. Some extensions to the quasi-convex, and semi-algebraic cases are considered. By time discretization, we make the link with recent studies concerning gradient-like algorithms for multi-objective optimization. Applications are given in signal/imaging processing, and Pareto equilibrium in cooperative games.