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A Lagrange duality approach for multi-composed optimization problems

Author

Listed:
  • Gert Wanka

    (Chemnitz University of Technology)

  • Oleg Wilfer

    (Chemnitz University of Technology)

Abstract

In this paper, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of $$n+1$$ 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.

Suggested Citation

  • Gert Wanka & Oleg Wilfer, 2017. "A Lagrange duality approach for multi-composed optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 288-313, July.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-016-0431-2
    DOI: 10.1007/s11750-016-0431-2
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    References listed on IDEAS

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    1. Radu Boţ & Christopher Hendrich, 2013. "A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems," Computational Optimization and Applications, Springer, vol. 54(2), pages 239-262, March.
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    Cited by:

    1. Sorin-Mihai Grad & Oleg Wilfer, 2019. "A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality," Journal of Global Optimization, Springer, vol. 74(1), pages 121-160, May.

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