On a Generalization of a Normal Map and Equation

Authors:
Jong-Shi Pang;Jen-Chih Yao
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1995

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Abstract

The class of normal maps was recently investigated by Robinson and Ralph in connection with the study of a variational inequality defined on a polyhedral set. In this paper a generalization of such a map is considered, and the associated generalized normal equation is studied. The latter provides a unified formulation of several generalized variational inequality and complementarity problems. Using degree theory, some sufficient conditions for the existence of a zero of a generalized normal map are established and the stability of a generalized normal equation at a solution is analyzed. Specializations of the results to various applications are discussed.