A closedness condition and its applications to DC programs with convex constraints
Dinh, N
T, T.A. Nghia
Vallet, G.
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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