Pham Dinh Tao; Le Thi Hoai An Convex analysis approach to d. c. programming: Theory, algorithms and applications. (English) Zbl 0895.90152 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. Cited in 3 ReviewsCited in 177 Documents 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 PDF BibTeX XML Cite \textit{Pham Dinh Tao} and \textit{Le Thi Hoai An}, Acta Math. Vietnam. 22, No. 1, 289--355 (1997; Zbl 0895.90152) OpenURL