This paper considers generalized equations, which are convenient tools for formulating problems in complementarity and in mathematical programming, as well as variational inequalities. We introduce a regularity condition for such problems and, with its help, prove existence, uniqueness and Lipschitz continuity of solutions to generalized equations with parametric data. Applications to nonlinear programming and to other areas are discussed, and for important classes of such applications the regularity condition given here is shown to be in a certain sense the weakest possible condition under which the stated properties will hold.

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We consider a class of " generalized equations ," involving point-to-set mappings , wh ich formulate the problems of linear and nonlinear programming and of complemen tari ty, among others. Solution sets of such generalized equations are shown to be stable under cer tain hypotheses ; in particular a general form of the implicit function theorem is proved for such problems . An application to linear generalized equations is given at the end of the paper; this covers linear and convex quadratic programming and the positive semidefinite linear complementarity problem . The general nonlinear programming problem is trea ted in Par t II of the pape r , using the method s developed here . AMS (MOS) Subject Classifications : 47805, 9OAl5 , 90C30.

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