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Level Function Method for Quasiconvex Programming

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  • H. Xu

Abstract

In this paper, we introduce the notion of level function for a continuous real-valued quasiconvex function. The existence, construction, and application of level functions are discussed. Further, we propose a numerical method based on level functions for the solution of quasiconvex minimization problems. Several versions of the algorithms are presented. Also, we apply the idea of the level function method to the solution of a class of variational inequality problems. Finally, the results of numerical experiments on the proposed algorithms are reported.

Suggested Citation

  • H. Xu, 2001. "Level Function Method for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 407-437, February.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:2:d:10.1023_a:1026446503110
    DOI: 10.1023/A:1026446503110
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    1. Lemaréchal, C. & Nemirovskii, A. & Nesterov, Y., 1995. "New variants of bundle methods," LIDAM Reprints CORE 1166, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. William B. Haskell & Wenjie Huang & Huifu Xu, 2018. "Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions," Papers 1805.06632, arXiv.org.
    2. Meskarian, Rudabeh & Xu, Huifu & Fliege, Jörg, 2012. "Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 216(2), pages 376-385.

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