A NONMONOTONE GRADIENT METHOD FOR CONSTRAINED MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this paper, we consider a nonmonotone gradient method for smooth constrained multiob-jective optimization problems. Under mild assumptions, we demonstrate the Pareto stationarity of the accumulation point of the sequence generated by this method, while the convergence of the full sequence to a weak Pareto optimal solution of the problem is proven when the function is convex. Further, by im-posing some assumptions on the gradients of the objective functions and the search directions, the linear convergence of the function value sequence to the optimal value is provided. The initial point in the convergence results established here can be any one in the constraint set.