Exceptional Families and Existence Theorems for Variational Inequality Problems

Y. B. Zhao, J. Y. Han and H. D. Qi
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Y. B. Zhao: Chinese Academy of Sciences
J. Y. Han: Chinese Academy of Sciences
H. D. Qi: Chinese Academy of Sciences

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 2, No 11, 475-495

Abstract: Abstract This paper introduces the concept of exceptional family for nonlinear variational inequality problems. Among other things, we show that the nonexistence of an exceptional family is a sufficient condition for the existence of a solution to variational inequalities. This sufficient condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. From the results in this paper, we believe that the concept of exceptional families of variational inequalities provides a new powerful tool for the study of the existence theory for variational inequalities.

Keywords: Variational inequalities; convex programming; complementarity problems; exceptional families; existence theorems (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (16)

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DOI: 10.1023/A:1021701913337

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