A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

Abstract

By using auxiliary principle technique, a new proximal point algorithm based on decomposition method is suggested for computing a weakly efficient solution of the constrained multiobjective optimization problem (MOP) without assuming the nonemptiness of its solution set. The optimality conditions for (MOP) are derived by the Lagrangian function of its subproblem and corresponding mixed variational inequality. Some basic properties and convergence results of the proposed method are established under some mild assumptions. As an application, we employ the proposed method to solve a split feasibility problem. Finally, numerical results are also presented to illustrate the feasibility of the proposed algorithm.

Proximal point algorithm for differentiable quasi-convex multiobjective optimization

“…Moreover, since F is differentiable, we have ∂ f i (x) = {∇ f i (x)}. Using the characterization (10) with h = • F and x =x, there exists a vector α = (α 1 , ..., α…”

“…Da Cruz Neto et al [11], extended the classical subgradient method from real-valued minimization to multiobjective optimization for solving quasiconvex nondifferentiable unconstrained multiobjective optimization problems. Chen et al [10] proposed a new proximal point algorithm by using auxiliary principle technique, based on decomposition method for computing a weakly efficient solution of the constrained multiobjective optimization problem without assuming the nonemptiness of its solution set.…”

A cooperative coevolution PSO technique for complex bilevel programming problems and application to watershed water trading decision making problems

“…During the past decades, some surveys and bibliographic reviews were given by several authors [11,12,15,41]. Reference books on bilevel programming and related issues have emerged [5,10,14,34,39].…”

Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points

“…Particularly, Pareto/weak efficient solution notions of vector optimization have been extensively studied; see [1,2,6,3,32,27]. In recent years, optimality conditions for optimization problems are widely studied since they play a crucial role in duality theory and algorithm design; see [1,7,8,9,10,28,33,34]. Basically, all optimality conditions are derived using theorem of separation and theorem of alterative or an adequate substitute such as Ekeland's principle; see [6,7,34,11,12,13].…”