Um método de gradiente não monótono para problemas de otimização multiobjetivo com restrições

Abstract

In this dissertation, we consider a nonmonotone gradient method for Multiobjective Optimization problems with smooth constraints. Under mild assumptions, we demons trate Pareto stationarity of the accumulation point of the sequence generated by this method, and we, prove the convergence of the full sequence to a weak Pareto optimal solution of the problem is proven when the function is convex. Further, imposing some assumptions on the gradients of the objective functions and the search directions, we provide the linear convergence of the function value sequence to the optimal value. The initial point, in the our convergence results established can be any one in the constraint set. Furthermore, we show the numerical results when applying this method.