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Generalized differentiation with positively homogeneous maps: Applications in set-valued analysis and metric regularity

C.H. Jeffrey Pang(chj2pang***at***math.uwaterloo.ca)

Abstract: We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between the Aubin property and coderivatives, and study how metric regularity and open covering can be refined to have a directional property similar to our concept of generalized differentiation. Finally, we discuss the relationship between the robust form of generalization differentiation and its one sided counterpart.

Keywords: multi-function differentiability, metric regularity, coderivatives, calmness, Lipschitz continuity.

Category 1: Convex and Nonsmooth Optimization (Other )

Citation: (Identical to http://arxiv.org/abs/0907.5439v3)

Download: [PDF]

Entry Submitted: 02/16/2010
Entry Accepted: 02/16/2010
Entry Last Modified: 02/16/2010

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