| In this thesis, we study error bounds for set inclusion systems and for conic convex inequality systems. In particular, we present the following: (1) Results on global error bounds in terms of various local error bounds. (2) Generalization of the Robinson-Ursescu Theorem to a normed space setting (instead of the Banach space setting). (3) Error bound results on an assumption similar to the Slater condition. (4) We prove the Li-Singer conjecture on the existence of error bounds (even under somewhat weaker assumption of Li-Singer). (5) Characterizations of error bounds in terms of the contingent derivative, Dini-derivative and the numerical derivative of multifunctions. (6) Explicit formulas of the least error bound in terms of the directional direvative and the coderivative. (7) Stability of error bounds. (8) Relationship among the fundamental concepts of the Basic Constraint Qualification (BCQ), the strong BCQ, the metric regularity and the error bounds.; For the special cases (such as for systems of finitely and/or infinitely many convex inequalities as well as systems of linear equalities) we recapture many known results as well as obtain new results on error bounds. In particular an open problem of Lewis and Pang on characterizing the existence of a local error bound in terms of normal cones is solved.{09}... |
