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Saddle points and gap functions for weak generalized Ky Fan inequalities

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Abstract

In this paper, we employ the image space analysis method to investigate a weak generalized Ky Fan inequality with cone constraints. Some regular weak separation functions are introduced, and generalized Lagrangian functions are constructed by using these regular weak separation functions. Under suitable convexity assumptions and Slater condition, the existence of solution for the weak generalized Ky Fan inequality with cone constraints is equivalent to a saddle point of the generalized Lagrangian functions. Moreover, we also use the regular weak separation functions to construct gap functions for the weak generalized Ky Fan inequality with cone constraints, and obtain its error bound.

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Acknowledgements

The authors thank the two anonymous reviewers for their valuable comments and suggestions, which helped to improve the paper. This research was supported by the National Natural Science Foundation of China (Grant Nos. 11171362, 11571055).

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

    G. H. Li & S. J. Li

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  1. G. H. Li
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  2. S. J. Li
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Correspondence to S. J. Li.

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Li, G.H., Li, S.J. Saddle points and gap functions for weak generalized Ky Fan inequalities. Optim Lett 12, 1265–1280 (2018). https://doi.org/10.1007/s11590-017-1118-9

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