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Horatiu-Vasile Boncea, Sorin-Mihai Grad: Characterizations of $ arepsilon$-duality gap statements for constrained optimization problems

Horatiu-Vasile Boncea, Sorin-Mihai Grad: Characterizations of $ arepsilon$-duality gap statements for constrained optimization problems

Author(s):
Horatiu-Vasile Boncea
Sorin-Mihai Grad
Title:
Horatiu-Vasile Boncea, Sorin-Mihai Grad: Characterizations of $ arepsilon$-duality gap statements for constrained optimization problems
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2012
Mathematics Subject Classification:
49N15 []
90C25 []
90C34 []
Abstract:
In this paper we present different regularity conditions that equivalently characterize various $\varepsilon$-duality gap statements (with $\varepsilon\geq 0$) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and $\varepsilon$-subdifferentials. When $\varepsilon=0$ we rediscover recent results on stable strong and total duality and zero duality gap from the literature.
Keywords:
Conjugate functions, $ arepsilon$-duality gap, constraint qualifications, Lagrange dual problems, Fenchel-Lagrange dual problems
Language:
English
Publication time:
12/2012