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Subsmooth semi-infinite and infinite optimization problems

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Abstract

We first consider subsmoothness for a function family and provide formulas of the subdifferential of the pointwise supremum of a family of subsmooth functions. Next, we consider subsmooth infinite and semi-infinite optimization problems. In particular, we provide several dual and primal characterizations for a point to be a sharp minimum or a weak sharp minimum for such optimization problems.

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Authors and Affiliations

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

    Xi Yin Zheng

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

    Kung Fu Ng

Authors
  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 an Earmarked Grant (GRF) from the Research Grant Council of Hong Kong and the National Natural Science Foundation of P. R. China (Grant No. 11061038).

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Zheng, X.Y., Ng, K.F. Subsmooth semi-infinite and infinite optimization problems. Math. Program. 134, 365–393 (2012). https://doi.org/10.1007/s10107-011-0440-8

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  • DOI: https://doi.org/10.1007/s10107-011-0440-8

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