Global error bounds with fractional exponents

Abstract.

Using the partial order induced by a proper weakly lower semicontinuous function on a reflexive Banach space X we give a sufficient condition for f to have error bounds with fractional exponents. Application is given to identify the set of such exponents for quadratic functions.

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Authors and Affiliations

1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong, e-mail: kfng@math.cuhk.edu.hk, HK

   Kung Fu Ng

2. Department of Mathematics, Yunnan University, Kunming 650091, P.R. China, e-mail: xyzheng@ynu.edu.cn, CN

   Xi Yin Zheng

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1. Kung Fu Ng
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2. Xi Yin Zheng
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Received: August 20, 1999 / Accepted: March 20, 2000¶Published online July 20, 2000

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Ng, K., Zheng, X. Global error bounds with fractional exponents. Math. Program. 88, 357–370 (2000). https://doi.org/10.1007/s101070050021

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• Published: 25 February 2014

• Issue Date: August 2000

• DOI: https://doi.org/10.1007/s101070050021

• Key words: error bound – lower semicontinuous function – convex function – quadratic function – reflexive Banach space Mathematics Subject Classification (1991): 90C31, 90C25, 49J52