Linear Stability of Generalized Equations Part I: Basic Theory

(Dedicated to Anthony V. Fiacco on the occasion of his 65th birthday.)

We consider a class of generalized equations involving set-valued maps, which formulate many problems from mathematical programming, complementarity theory and mathematical economics. Many results concerning the stability behavior of the solution sets of this class of generalized equations have been established, mainly focusing on “qualitative” characterizations. We develop a theory concentrating on “quantitative” characterizations of the stability behavior of solutions of generalized equations, and establish conditions which ensure the solution set of a generalized equation is “quantitatively” stable. In Part II of the paper, we use the concepts and methods developed here to treat norlinear programming problems.