CONVERGENCE ANALYSIS OF A PROJECTED GRADIENT METHOD FOR MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this paper, we consider a projected gradient method for constrained multiobjective opti-mization problems. Under suitable assumptions, we show that the sequence generated by the method converges to a Pareto stationary point (or a weak Pareto optimal point) of the problem when the mul-tiobjective function is quasiconvex (or pseudoconvex). Furthermore, in the case that the multiobjective function is convex, by using some approximate conditions that are imposed on the gradients of the ob-jective functions and the search directions, we obtain the linear convergence result for this method.