Proximal point algorithm for differentiable quasi-convex multiobjective optimization

Abstract

The main aim of this paper is to consider the proximal point method for solving multiobjective optimization problem under the differentiability, locally Lipschitz and quasi-convex conditions of the objective function. The control conditions to guarantee that the accumulation points of any generated sequence, are Pareto critical points are provided.

The PPADMM Method for Solving Quadratic Programming Problems

“…where F ∈ R n×n , G ∈ R m×m are symmetric positive semidefinite matrices and f ∈ R n , g ∈ R m are the known vectors. The class of convex minimization problems arises in many areas of computational science and engineering applications such as compressed sensing [1], financial [2,3], image restoration [4][5][6], network optimization problems [7,8], and traffic planning convex problems [9][10][11][12]. The model ( 1)-(2) captures many applications in different areas-see the l1-norm regularized least-squares problems in [12,13], the total variation image restoration in [13][14][15][16], and the standard quadratic programming problems in [7,13].…”