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Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes

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Abstract

In the first part of this paper series, a unified duality scheme for a constrained extremum problem is proposed by virtue of the image space analysis. In the present paper, we pay our attention to study of some special duality schemes. Particularly, the Lagrange-type duality, Wolfe duality and Mond–Weir duality are discussed as special duality schemes in a unified interpretation. Moreover, three practical classes of regular weak separation functions are also considered.

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Acknowledgements

The authors are grateful to the two anonymous referees and Professor F. Giannessi for their valuable comments and suggestions, especially for providing the references [12, 14, 15], which helped to improve the paper. This research was supported by the National Natural Science Foundation of China (Grant: 11171362) and the Basic and Advanced Research Project of CQCSTC (Grant: cstc2013jcyjA00003).

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

    S. K. Zhu & S. J. Li

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Zhu, S.K., Li, S.J. Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes. J Optim Theory Appl 161, 763–782 (2014). https://doi.org/10.1007/s10957-013-0467-5

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