OPTIMALITY CONDITIONS OF QUASI (α, ε)-SOLUTIONS AND APPROXIMATE MIXED TYPE DUALITY FOR DC COMPOSITE OPTIMIZATION PROBLEMS

This paper is devoted to the approximate optimality condition and mixed type duality for DC composite optimization problems in locally convex Hausdorff topological vector spaces. By using the properties of the Fre acute accent chet subdifferential, a new constraint qualification is introduced. Under this constraint qualification, some approximate optimality conditions of the quasi (alpha, epsilon)-optimal solution for DC compose optimization problem and associated mixed type duality theorems are established, which extend and improve the corresponding results in the previous papers.

Automated summary

This paper is focused on the approximate optimality condition and mixed type duality for DC composite optimization problems in locally convex Hausdorff topological vector spaces. A new constraint qualification is introduced based on the properties of the Fre acute accent chet subdifferential. Under this constraint qualification, approximate optimality conditions for the quasi (alpha, epsilon)-optimal solution and associated mixed type duality theorems are established, which improve and extend the previous results.