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Strong KKT conditions and weak sharp solutions in convex-composite optimization

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Abstract

Using variational analysis techniques, we study convex-composite optimization problems. In connection with such a problem, we introduce several new notions as variances of the classical KKT conditions. These notions are shown to be closely related to the notions of sharp or weak sharp solutions. As applications, we extend some results on metric regularity of inequalities from the convex case to the convex-composite case.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, 650091, Kunming, People’s Republic of China

    Xi Yin Zheng

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong

    Kung Fu Ng

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  1. Xi Yin Zheng
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  2. Kung Fu Ng
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Correspondence to Xi Yin Zheng.

Additional information

This research was supported by the National Natural Science Foundation of P. R. China (10761012) and an Earmarked Grant from the Research Grant Council of Hong Kong.

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Zheng, X.Y., Ng, K.F. Strong KKT conditions and weak sharp solutions in convex-composite optimization. Math. Program. 126, 259–279 (2011). https://doi.org/10.1007/s10107-009-0277-6

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