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

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.

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

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