A nonmonotone gradient method for constrained multiobjective optimization problems

Abstract

In this paper, we consider a nonmonotone gradient method for smooth constrained multiobjective 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 imposing 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.

An Approximation Method for Variational Inequality with Uncertain Variables

“…Through the unremitting efforts of many mathematicians, VIP has developed into an important subject with rich content and broad prospects in mathematical programming. These achievements involve rich mathematical theories, optimization theory, economics and engineering (see [1][2][3][4][5][6][7]), and so on. For the classical VIP, ∀v ∈ S, there is a point u ∈ S ∈ R n such that…”