NDLI: Duality and optimality conditions for generalized equilibrium problems involving DC functions

Content Provider	Springer Nature Link
Author	Dinh, N. Strodiot, J. J. Nguyen, V. H.
Copyright Year	2009
Abstract	We consider a generalized equilibrium problem involving DC functions which is called (GEP). For this problem we establish two new dual formulations based on Toland-Fenchel-Lagrange duality for DC programming problems. The first one allows us to obtain a unified dual analysis for many interesting problems. So, this dual coincides with the dual problem proposed by Martinez-Legaz and Sosa (J Glob Optim 25:311–319, 2006) for equilibrium problems in the sense of Blum and Oettli. Furthermore it is equivalent to Mosco’s dual problem (Mosco in J Math Anal Appl 40:202–206, 1972) when applied to a variational inequality problem. The second dual problem generalizes to our problem another dual scheme that has been recently introduced by Jacinto and Scheimberg (Optimization 57:795–805, 2008) for convex equilibrium problems. Through these schemes, as by products, we obtain new optimality conditions for (GEP) and also, gap functions for (GEP), which cover the ones in Antangerel et al. (J Oper Res 24:353–371, 2007, Pac J Optim 2:667–678, 2006) for variational inequalities and standard convex equilibrium problems. These results, in turn, when applied to DC and convex optimization problems with convex constraints (considered as special cases of (GEP)) lead to Toland-Fenchel-Lagrange duality for DC problems in Dinh et al. (Optimization 1–20, 2008, J Convex Anal 15:235–262, 2008), Fenchel-Lagrange and Lagrange dualities for convex problems as in Antangerel et al. (Pac J Optim 2:667–678, 2006), Bot and Wanka (Nonlinear Anal to appear), Jeyakumar et al. (Applied Mathematics research report AMR04/8, 2004). Besides, as consequences of the main results, we obtain some new optimality conditions for DC and convex problems.
Starting Page	183
Ending Page	208
Page Count	26
File Format	PDF
ISSN	09255001
Journal	Journal of Global Optimization
Volume Number	48
Issue Number	2
e-ISSN	15732916
Language	English
Publisher	Springer US
Publisher Date	2009-11-08
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Equilibrium problems Duality Fenchel conjugation DC functions Variational inequalities Optimization Real Functions Computer Science Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Management Science and Operations Research Business, Management and Accounting Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Duality for Equilibrium Problems

Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces

Semi-continuous quadratic optimization: existence conditions and duality scheme

Existence theorem for a class of generalized quasi-variational inequalities

Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems

Existence Results for Systems of Vector Equilibrium Problems*

An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems

Nonmonotone equilibrium problems: coercivity conditions and weak regularization

Optimality and duality in vector optimization involving generalized type I functions over cones

Duality and optimality conditions for generalized equilibrium problems involving DC functions

Similar Documents

Duality for Equilibrium Problems

Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces

Semi-continuous quadratic optimization: existence conditions and duality scheme

Existence theorem for a class of generalized quasi-variational inequalities

Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems

Existence Results for Systems of Vector Equilibrium Problems*

An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems

Nonmonotone equilibrium problems: coercivity conditions and weak regularization

Optimality and duality in vector optimization involving generalized type I functions over cones

Duality and optimality conditions for generalized equilibrium problems involving DC functions