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A Lagrange duality approach for multi-composed optimization problems

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Gert Wanka & Oleg Wilfer

Authors
  1. Gert Wanka
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  2. Oleg Wilfer
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Correspondence to Gert Wanka.

Additional information

This work was supported by the DFG (the German Research Foundation) under Project WA922/8-1.

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Wanka, G., Wilfer, O. A Lagrange duality approach for multi-composed optimization problems. TOP 25, 288–313 (2017). https://doi.org/10.1007/s11750-016-0431-2

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  • DOI: https://doi.org/10.1007/s11750-016-0431-2

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