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Zbl 0891.90132
Li, Wu
Abadie's constraint qualification, metric regularity, and error bounds for differentiable convex inequalities. (English)
[J] SIAM J. Optim. 7, No.4, 966-978 (1997). ISSN 1052-6234; ISSN 1095-7189/e

Summary: We study differentiable convex inequalities and prove that metric regularity and Abadie's constraint qualification (CQ) are equivalent for such inequalities. For convex quadratic inequalities, we show that metric regularity, the existence of a global error bound, and Abadie's CQ are mutually equivalent. As a consequence, we derive two new characterizations of weak sharp minima of a convex quadratic programming problem.

MSC 2000:: *90C20 Quadratic programming
90C30 Nonlinear programming

Keywords: differentiable convex inequalities; Abadie's constraint qualification; convex quadratic inequalities; convex quadratic programs; error bounds; metric regularity; weak sharp minima

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