Proximal Gradient Algorithm And Application For Non-smooth Multi-objective Optimization Problems

Multi-objective optimization is an important method to solve economic and management problems.In this thesis,a novel proximal gradient method(NPGM)for solving nonsmooth multiobjective optimization problems is introduced by the non-monotone linear search technique allowing the increase of objective function values in some iterative process.The level-bounded notion of vector-valued function and a new assumption are also presented.The asymptotical characterizations of the corresponding sequences generated by(NPGM)are obtained under some mild conditions.We further establish the global convergence of the iterative sequence generated by(NPGM)and the sufficient condition for the existence of Pareto critical point which is the accumulation point of the iterative sequence.As an application,we present a tractable second-order cone programming formulation of robust multiobjective optimization problem(RMOP)by the constraint scalarization method,and then the(RMOP)is also solved by(NPGM).Besides,some numerical experiments are reported to show the feasibility and efficiency of(NPGM)for solving multiobjective optimization problems.Finally,based on(NPGM)algorithm,by further relaxing the Armijo type line search conditions in non-monotone line search,A new proximal gradient method(NNPGM)for solving non-smooth multiobjective optimization problems is proposed.Based on the framework of analyzing the convergence of the algorithm(NPGM),we also establish the global convergence of the iterative sequences generated by(NNPGM)and the sufficient conditions to obtain the Pareto critical point.Finally,some numerical experiments are reported to show the feasibility and efficiency of(NNPGM)for solving multiobjective optimization problems as well.