Applied Set-Valued Analysis and Optimization

Full Text: PDF
DOI: 10.23952/asvao.7.2025.1.05
Volume 7, Issue 1, 1 April 2025, Pages 71-91

 

Abstract. We investigate constrained optimization problems involving difference of convex functions in the objective as well as in the constraint functions. We first associate with the considered problem a parametric convex one. Relations between the two problems are analyzed, and necessary optimality conditions are given for such problems. Using the parametric approach, we propose three kinds of methods. The first one, we call the DC method of centers, generates a sequence of convex problems that incorporate the constraints in their objective functions. The second one is a pure proximal point method, based on the DC method of centers and the proximal point algorithm idea. The third one is a family of proximal bundle methods that combine the previous cited parametric approach, the proximal point algorithm idea, and the bundle concept. These methods are globally convergent in the sense that they converge for every starting point, feasible, or infeasible. We show that every cluster point of the sequence of optimal solutions of these problems satisfies necessary optimality conditions of KKT criticality type. Finally, we end with some numerical tests to illustrate the behavior of the algorithm.

 

How to Cite this Article:
K. Boufi, A. Fadil, A. Roubi, Algorithms for solving optimization programs involving difference of convex functions, Appl. Set-Valued Anal. Optim. 7 (2025), 71-91.