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Optimality condition and complexity of order-value optimization problems and low order-value optimization problems

Author

Listed:
  • Zhongyi Jiang

    (Fudan University
    Changzhou University)

  • Qiying Hu

    (Fudan University)

  • Xiaojin Zheng

    (Tongji University)

Abstract

Order-value optimization problems and low order-value optimization problems are new subclasses of optimization problems which arise from decision-making problems under uncertainty and robust estimation problems. In this paper, We present KKT necessary and sufficient conditions for low order-value optimization problems under convexity hypothesis in this paper. A smooth reformulation of low order-value optimization problems are presented whose local solutions satisfy the KKT necessary conditions. we prove that order-value optimization problems is NP-hard in the strong sense even when constraints are polytope. Order-value optimization problems and low order-value optimization problems are NP-hard even when their presentation functions are linear and constraints are polytope. Some special cases that could be solved in polynomial time are proposed.

Suggested Citation

  • Zhongyi Jiang & Qiying Hu & Xiaojin Zheng, 2017. "Optimality condition and complexity of order-value optimization problems and low order-value optimization problems," Journal of Global Optimization, Springer, vol. 69(2), pages 511-523, October.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0520-2
    DOI: 10.1007/s10898-017-0520-2
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    References listed on IDEAS

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    1. Roberto Andreani & Cibele Dunder & José Mario Martínez, 2003. "Order-Value Optimization: Formulation and solution by means of a primal cauchy method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 387-399, December.
    2. José Martínez, 2012. "Generalized order-value optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 75-98, April.
    3. E. Birgin & L. Bueno & N. Krejić & J. Martínez, 2011. "Low order-value approach for solving VaR-constrained optimization problems," Journal of Global Optimization, Springer, vol. 51(4), pages 715-742, December.
    4. R. Andreani & C. Dunder & J. Martínez, 2005. "Nonlinear-programming reformulation of the order-value optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 365-384, July.
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    Cited by:

    1. E. V. Castelani & R. Lopes & W. V. I. Shirabayashi & F. N. C. Sobral, 2021. "A robust method based on LOVO functions for solving least squares problems," Journal of Global Optimization, Springer, vol. 80(2), pages 387-414, June.

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