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Levitin–Polyak well-posedness by perturbations of inverse variational inequalities

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Abstract

The purpose of this paper is to investigate Levitin–Polyak type well-posedness for inverse variational inequalities. We establish some metric characterizations of Levitin–Polyak α-well-posedness by perturbations. Under suitable conditions, we prove that Levitin–Polyak well-posedness by perturbations of an inverse variational inequality is equivalent to the existence and uniqueness of its solution. Moreover, we show that Levitin–Polyak well-posedness by perturbations of an inverse variational inequality is equivalent to Levitin–Polyak well-posedness by perturbations of an enlarged classical variational inequality.

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Authors and Affiliations

  1. Department of Mathematics, Chengdu University of Information Technology, Chengdu, 610225, Sichuan, People’s Republic of China

    Rong Hu

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Rong Hu & Ya-Ping Fang

Authors
  1. Rong Hu
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  2. Ya-Ping Fang
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Correspondence to Ya-Ping Fang.

Additional information

This work was supported by the National Natural Science Foundation of China (11001187) and the Scientific Research Foundation of CUIT(KYTZ201128).

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Hu, R., Fang, YP. Levitin–Polyak well-posedness by perturbations of inverse variational inequalities. Optim Lett 7, 343–359 (2013). https://doi.org/10.1007/s11590-011-0423-y

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  • DOI: https://doi.org/10.1007/s11590-011-0423-y

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