Sorin-Mihai Grad, Oleg Wilfer, Gert Wanka: Duality and epsilon-optimality conditions for multi-composed optimization problems with applications to fractional and entropy optimization

Author(s):

Sorin-Mihai Grad
Oleg Wilfer
Gert Wanka

Title:

Sorin-Mihai Grad, Oleg Wilfer, Gert Wanka: Duality and epsilon-optimality conditions for multi-composed optimization problems with applications to fractional and entropy optimization

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 04, 2016

Mathematics Subject Classification:

    49N15 []
    90C25 []
    90C46 []

Abstract:

We introduce a closedness type regularity condition that characterizes the stable strong duality for convex constrained optimization problems with multi-composed objective functions and guarantees a formula for the epsilon-subdifferential of a multi-composed function, that is employed for delivering necessary and sufficient epsilon-optimality conditions that characterize $\varepsilon$-optimality solutions to multi-composed optimization problems. As a byproduct, a formula of the conjugate function of a multi-composed function is provided under a regularity condition weaker than known in the literature. We also present two possible applications of our investigations in fractional programming and entropy optimization, respectively.

Keywords:

convex functions, composed functions, regularity conditions, conjugate functions, fractional programming, entropy optimization

Language:

English

Publication time:

7/2016