Conical open mapping theorems and regularity

Bauschke, Heinz H. and Borwein, Jonathan M. (1999) Conical open mapping theorems and regularity. In: Proceedings of the Centre for Mathematics and its Applications (Australian National University) , March 1998, National Symposium on Functional Analysis, Optimization and Applications.

 Preview
Postscript
Download (270Kb) | Preview
 Preview
PDF
Download (244Kb) | Preview

Abstract

Suppose $T$ is a continuous linear operator between two Hilbert spaces $X$ and $Y$ and let $K$ be a closed convex nonempty cone in $X$. We investigate the possible existence of $\delta > 0$ such that $\delta B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $B_X,B_Y$ denote the closed unit balls in $X$ and $Y$ respectively. This property, which we call openness relative to $K$, is a generalization of the classical openness of linear operators. We relate relative openness to Jameson's property~(G), to the strong conical hull intersection property, to bounded linear regularity, and to metric regularity. Our results allow a simple construction of two closed convex cones that have the strong conical hull intersection property but fail to be boundedly linearly regular.

Item Type: Conference or Workshop Item (Paper) pubdom FALSE bounded linear regularity, linear regularity, conical hull intersection property, metric regularity, normal cone, open mapping theorem, property (G), strong CHIP, strong conical hull intersection property 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming47-xx Operator theory > 47Bxx Special classes of linear operators49-xx Calculus of variations and optimal control; optimization > 49Nxx Miscellaneous topics52-xx Convex and discrete geometry > 52Axx General convexity UNSPECIFIED Users 1 not found. 25 Nov 2003 01 Mar 2015 17:29 https://docserver.carma.newcastle.edu.au/id/eprint/208

Actions (login required)

 View Item