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Nonlinear separation functions and constrained extremum problems

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Abstract

In this paper, the image space analysis is employed to investigate constrained extremum problems. A new nonlinear separation function for the constrained extremum problems is given. Some optimality conditions and a strong duality theorem for the constrained extremum problem are obtained. These results extend and improve the corresponding ones in the literature.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant Number: 11171362). The authors would like to thank the anonymous reviewer for his valuable comments and suggestions, which helped to improve the paper.

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Authors and Affiliations

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

    Y. D. Xu & S. J. Li

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  1. Y. D. Xu
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  2. S. J. Li
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Correspondence to Y. D. Xu.

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Xu, Y.D., Li, S.J. Nonlinear separation functions and constrained extremum problems. Optim Lett 8, 1149–1160 (2014). https://doi.org/10.1007/s11590-013-0644-3

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  • DOI: https://doi.org/10.1007/s11590-013-0644-3

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