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
