Linear stability of generalized equations. Part I: Basic theory

The paper considers 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. The paper develops a theory concentrating on ‘quantitative’ characterizations of the stability behavior of solutions of generalized equations, and establishes conditions which ensure the solution set of a generalized equation is ‘quantitatively’ stable. In Part II of the paper, it uses the concepts and methods developed here to treat nonlinear programming problems.