A closedness condition and its applications to DC programs with convex constraints

Dinh, N
T, T.A. Nghia
Vallet, G.
This paper concerns a closedness condition called (CC) involving a convex function and a convex constrained system. This type of condition has played an important role in the study of convex optimization problems. Our aim is to establish several characterizations of this condition and to apply them to study problems of minimizing a DC function under a cone-convex constraint and a set constraint. First, we establish several so-called 'Toland-Fenchel-Lagrange' duality theorems. As consequences, various versions of generalized Farkas lemmas in dual forms for systems involving convex and DC functions are derived. Then, we establish optimality conditions for DC problem under convex constraints. Optimality conditions for convex problems and problems of maximizing a convex function under convex constraints are given as well. Most of the results are established under the (CC) condition. This article serves as a link between several corresponding known ones published recently for DC programs and for convex programs.
Chi tiết xin mời tham khảo tại http://repository.vnu.edu.vn/handle/VNU_123/29106 
Title: A closedness condition and its applications to DC programs with convex constraints
Authors: Dinh, N
T, T.A. Nghia
Vallet, G.
Keywords: DC programs;Closedness conditions;Closed-cone constraint qualification;Farkas lemmas;Fenchel-Lagrange duality;Lagrange duality
Issue Date: 2010
Publisher: TAYLOR & FRANCIS LTD, 4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND
Citation: ISIKNOWLEDGE
Description: TNS06224 ; OPTIMIZATION Volume: 59 Issue: 4 Pages: 541-560
URI: http://repository.vnu.edu.vn/handle/VNU_123/29106
http://www.tandfonline.com/doi/abs/10.1080/02331930801951348
ISSN: 0233-1934
Appears in Collections:Bài báo của ĐHQGHN trong Web of Science

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