Levitin-Polyak well-posedness for variational inequalitiesand for optimization problems with variational inequalityconstraints

Rong Hu; Ya-Ping Fang; Nan-Jing Huang

doi:10.3934/jimo.2010.6.465

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2010, Volume 6, Issue 3: 465-481. Doi: 10.3934/jimo.2010.6.465

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Levitin-Polyak well-posedness for variational inequalities and for optimization problems with variational inequality constraints

1.
Department of Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225
2.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064

Received: April 30, 2009

Revised: February 28, 2010

Published: June 2010

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Abstract

In this paper, we study the Levitin-Polyak type well-posedness of variational inequalities and optimization problems with variational inequality constraints in Banach spaces. We derive some criteria and characterizations for these Levitin-Polyak well-posedness. We also investigate conditions under which the existence and uniqueness of solution is equivalent to the Levitin-Polyak well-posedness of the problem.

Keywords:

Variational inequality,
optimization problem with variational inequality constraints,
Levitin-Polyak well-posedness,
metric characterization,
uniqueness.

Mathematics Subject Classification: Primary: 90C31, 49J40; Secondary: 49K40.

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