Gert Wanka, Oleg Wilfer: A Lagrange Duality Approach for Multi-Composed Optimization Problems

Author(s):

Gert Wanka
Oleg Wilfer

Title:

Gert Wanka, Oleg Wilfer: A Lagrange Duality Approach for Multi-Composed Optimization Problems

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2015

Mathematics Subject Classification:

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

Abstract:

In this paper we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we calculate its conjugate dual problem, where the functions involved in the objective function of the primal problem will be decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulas of the conjugate as well as the biconjugate of the objective function of the primal problem and discuss an optimization problem having as objective function the sum of reciprocals of concave functions.

Keywords:

Lagrange Duality, Composed Functions, Generalized Interior Point Regularity Conditions, Conjugate Functions, Reciprocals of Concave Functions, Power Functions

Language:

English

Publication time:

07/2015