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Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential.

Dmitriy Drusvyatskiy(dd379***at***cornell.edu)
Adrian S. Lewis(aslewis***at***orie.cornell.edu)

Abstract: We prove that uniform second order growth, tilt stability, and strong metric regularity of the subdifferential --- three notions that have appeared in entirely different settings --- are all essentially equivalent for any lower-semicontinuous, extended-real-valued function.

Keywords: Tilt stability, variational analysis, subdifferentials, quadratic growth, strong metric regularity, prox-regularity

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Cornell University, School of Operations Research and Information Engineering, 206 Rhodes Hall Cornell University Ithaca, NY 14853. May 2012.

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Entry Submitted: 05/08/2012
Entry Accepted: 05/08/2012
Entry Last Modified: 05/08/2012

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