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Linear and nonlinear error bounds for lower semicontinuous functions

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Abstract

In this paper, we give some characterizations of linear and nonlinear error bounds for lower semicontinuous functions by a new notion, called subslope. And, extend some results of Azé and Corvellec (SIAM J Optim 12:913–927, 2002) and Corvellec and Motreanu (Math Program Ser A 114:291–319, 2008) slightly. Furthermore, we get a sufficient and necessary condition for global linear error bounds.

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Acknowledgments

The authors would like to thank the anonymous referees for their constructive comments and valuable suggestions which greatly improved the paper.

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  1. Department of Mathematics, Beijing University of Technology, 100124 , Beijing, China

    Mian-tao Chao & Cao-zong Cheng

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  1. Mian-tao Chao
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  2. Cao-zong Cheng
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Correspondence to Cao-zong Cheng.

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Chao, Mt., Cheng, Cz. Linear and nonlinear error bounds for lower semicontinuous functions. Optim Lett 8, 1301–1312 (2014). https://doi.org/10.1007/s11590-013-0648-z

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  • DOI: https://doi.org/10.1007/s11590-013-0648-z

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