Piecewise smoothness, local invertibility, and parametric analysis of normal maps
This paper is concerned primarily with properties of the Euclidean projection map onto a convex set defined by finitely many smooth, convex inequalities and affine equalities. A constant rank constraint qualification is assumed. It follows that the projection map is piecewise smooth (PC) hence B(ouligand)-differentiable; and a new, relatively simple, and computationally tractable formula is given for the B-derivative. These properties of the projection map are used to obtain inverse and implicit function theorems for associated normal maps, using a new characterization of invertibility of a PC Function in terms of its B-derivative. An extension of the implicit function theorem which does not require local uniqueness is also presented. Degree theory plays a major role in the analysis of both the locally unique case and its extension.
- OSTI ID:
- 36362
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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