CONVERGENCE OF A NEW NONMONOTONE MEMORY GRADIENT METHOD FOR UNCONSTRAINED MULTIOBJECTIVE OPTIMIZATION VIA ROBUST APPROACH

Robust approach is a special scalarization method to deal with multiobjective optimization problems in the worst-case. In this paper, we propose a new non-monotone gradient type algorithm for solving unconstrained multiobjective optimization problems by the conjugate technique and the robust approach. The proposed method has a memory gradient property since the search direction is constructed by using the current descent direction and the past multi-step iterative descent directions. For this, the search direction is called a memory gradient search direction. The step-size is computed by the nonmonotone linear search. A lower bound of the stepsize is presented under some mild conditions. Then the iterative sequence generated by the proposed method is proved to be convergent to a Pareto critical point of the multiobjective optimization problem under some mild conditions. Numerical experiments are reported to show the effectiveness of the proposed method.