Convex analysis approach to d. c. programming: Theory, algorithms and applications. (English) Zbl 0895.90152

Pham Dinh Tao; Le Thi Hoai An

Acta Math. Vietnam. 22, No. 1, 289-355 (1997).

Summary: This paper is devoted to a thorough study on convex analysis approach to d.c. (difference of convex functions) programming and gives the state of the art. Main results about d.c. duality, local and global optimalities in d.c. programming are presented. These materials constitute the basis of the DCA (d.c. algorithms). Its convergence properties have been tackled in detail, especially in d.c. polyhedral programming where it has finite convergence. Exact penalty, Lagrangian duality without gap, and regularization techniques have been studied to find appropriate d.c. decompositions and to improve consequently the DCA. Finally we present the application of the DCA to solving a lot of important real-life d.c. programs.

MSC:

90C25	Convex programming
49J52	Nonsmooth analysis
90C26	Nonconvex programming, global optimization

Keywords:

difference of convex functions; d.c. algorithms; convex analysis; d.c. polyhedral programming