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Conjugate duality for constrained optimization via image space analysis and abstract convexity

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Abstract

This paper is aimed at establishing a conjugate duality for the constrained optimizations equipped with some topical structures. First, we provide a dual problem for the general constrained optimization, discussing the weak duality as well as the strong duality based on the theory of abstract convexity. Transforming the zero duality gap property into a separation of two sets in image space, we involve the approach inspired by the image space analysis to study the dual theory by the aid of some separation functions. Then, using these results, we investigate this dual frame for the problem with some topical properties.

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Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (Grants: 11571055 and 11601437 ), the Fundamental Research Funds for the Central Universities (Grant Number: 106112017CD-JZRPY0020) and Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant Number: KJ1501503).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    C. L. Yao & S. J. Li

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  1. C. L. Yao
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  2. S. J. Li
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Correspondence to S. J. Li.

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Yao, C.L., Li, S.J. Conjugate duality for constrained optimization via image space analysis and abstract convexity. Optim Lett 13, 349–366 (2019). https://doi.org/10.1007/s11590-018-1365-4

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  • DOI: https://doi.org/10.1007/s11590-018-1365-4

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