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

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

Author(s):
Horatiu-Vasile Boncea
Sorin-Mihai Grad
Title:
Horatiu-Vasile Boncea, Sorin-Mihai Grad: Characterizations of $ arepsilon $-duality gap statements for composed optimization problems
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2012
Mathematics Subject Classification:
49N15 []
90C25 []
90C34 []
Abstract:
In this paper we present different regularity conditions that equivalently characterize $\varepsilon$-duality gap statements for optimization problems consisting of minimizing the sum of a function with the precomposition of a cone-increasing function to a vector function. These regularity conditions are formulated by using epigraphs and $\varepsilon$-subdifferentials. Taking $\varepsilon=0$ one can rediscover recent results on stable strong and total duality and zero duality gap from the literature. Moreover, as byproducts we deliver $\varepsilon $-optimality conditions and $(\varepsilon,\eta)$-saddle point statements for the mentioned type of problems, and $\varepsilon$-Farkas statements involving the sum of a function with the precomposition of a cone-increasing function to a vector function.
Keywords:
Conjugate functions, $ arepsilon$-duality gap, constraint qualifications, Fenchel-Lagrange dual
Language:
English
Publication time:
12/2012