# American Institute of Mathematical Sciences

July  2010, 6(3): 465-481. doi: 10.3934/jimo.2010.6.465

## 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, China 2 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received  May 2009 Revised  March 2010 Published  June 2010

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.
Citation: Rong Hu, Ya-Ping Fang, Nan-Jing Huang. Levitin-Polyak well-posedness for variational inequalities and for optimization problems with variational inequality constraints. Journal of Industrial & Management Optimization, 2010, 6 (3) : 465-481. doi: 10.3934/jimo.2010.6.465
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