A weighting subgradient algorithm for multiobjective optimization

We propose a weighting subgradient algorithm for solving multiobjective minimization problems on a nonempty closed convex subset of an Euclidean space. This method combines weighting technique and the classical projected subgradient method, using a divergent series steplength rule. Under the assumption of convexity, we show that the sequence generated by this method converges to a Pareto optimal point of the problem. Some numerical results are presented.