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Optimality condition and quasi-conjugate duality with zero gap in nonconvex optimization

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Abstract

In this article, we present an optimality condition in the form of a generalized KKT for nonconvex scalar-minimization problems. On the basis of the optimality condition, we present a quasi-conjugate duality for nonconvex scalar-minimization and vector-minimization problems. The duality is symmetric and has zero gap.

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Acknowledgements

We are very grateful to two anonymous referees for their really helpful and constructive comments that helped us very much in improving the paper. This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2019.303.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Pham Ngoc Anh

  2. Electric Power University, Hanoi, Vietnam

    Tran Van Thang

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  1. Pham Ngoc Anh
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  2. Tran Van Thang
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Correspondence to Pham Ngoc Anh.

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Anh, P.N., Van Thang, T. Optimality condition and quasi-conjugate duality with zero gap in nonconvex optimization. Optim Lett 14, 2021–2037 (2020). https://doi.org/10.1007/s11590-019-01523-9

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  • DOI: https://doi.org/10.1007/s11590-019-01523-9

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