On the Existence of Strong Unicity of Arbitrarily Small Order.

Abadie's Constraint Qualification, Hoffman's Error Bounds, and Hausdorff Strong Unicity

“…In this section, we show that Hausdorff strong unicity corresponds to Hoffman's error bounds for approximate solutions of convex quadratic inequalities (7). Then by using the reformulation (7) of (2) and a result on Hoffman's error bounds for convex quadratic inequalities [25], we prove that P G ( f ) is always Hausdorff strongly unique of order 2 m+1 .…”

“…Schmidt also used Theorem 7(viii) in this paper with $=1 and :=2 as the definition of strong unicity of order 1 2 . Meanwhile, Chalmers and Taylor [7] used (4) as the definition of strong unicity of order 1Â:. Theorem 7 in this paper contains many different yet equivalent formulations of Hausdorff strong unicity of order :, some of which were called local strong unicity when P G ( f ) is a singleton (cf.…”