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Quasiconjugate duality and optimality conditions for quasiconvex optimization

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  • Satoshi Suzuki

    (Shimane University)

Abstract

In nonlinear optimization, conjugate functions and subdifferentials play an essential role. In particular, Fenchel conjugate is the most well known conjugate function in convex optimization. In quasiconvex optimization, extra parameters for quasiconjugate functions have been introduced in order to show duality theorems, for example $$\lambda $$ λ -quasiconjugate and $$\lambda $$ λ -semiconjugate. By these extra parameters, we can show duality results that hold for general quasiconvex objective functions. On the other hand, extra parameters usually increase the complexity of dual problems. Hence, conjugate functions without extra parameters have also been investigated, for example H-quasiconjugate, R-quasiconjugate, and so on. However, there are some open problems. In this paper, we study quasiconjugate duality and optimality conditions for quasiconvex optimization without extra parameters. We investigate three types of quasiconjugate dual problems, and show sufficient conditions for strong duality. We introduce three types of quasi-subdifferentials, and study optimality conditions and characterizations of the solution set. Additionally, we give a classification of quasiconvex optimization problems in terms of quasiconjugate duality.

Suggested Citation

  • Satoshi Suzuki, 2025. "Quasiconjugate duality and optimality conditions for quasiconvex optimization," Journal of Global Optimization, Springer, vol. 92(2), pages 279-293, June.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:2:d:10.1007_s10898-024-01455-4
    DOI: 10.1007/s10898-024-01455-4
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    References listed on IDEAS

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    1. Satoshi Suzuki, 2010. "Set containment characterization with strict and weak quasiconvex inequalities," Journal of Global Optimization, Springer, vol. 47(2), pages 273-285, June.
    2. Satoshi Suzuki & Daishi Kuroiwa, 2015. "Characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 62(3), pages 431-441, July.
    3. Satoshi Suzuki & Daishi Kuroiwa, 2009. "Set containment characterization for quasiconvex programming," Computational Optimization and Applications, Springer, vol. 45(4), pages 551-563, December.
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