A nonmonotone gradient method for constrained multiobjective optimization problems
Journal of Nonlinear and Variational Analysis · 2022
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.