American Institute of Mathematical Sciences

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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

Rong Hu 1, , Ya-Ping Fang 2, and  Nan-Jing Huang 2,

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.
Keywords: metric characterization, uniqueness., Levitin-Polyak well-posedness, optimization problem with variational inequality constraints, Variational inequality.
Mathematics Subject Classification: Primary: 90C31, 49J40; Secondary: 49K4.
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 and Management Optimization, 2010, 6 (3) : 465-481. doi: 10.3934/jimo.2010.6.465
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