On partial smoothness, tilt stability and the VU-decomposition

Under the assumption of prox-regularity and the presence of a tilt stable local minimum we are able to show that a VU like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function.

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Bibliographic Details
Published in:	Mathematical programming Vol. 175; no. 1-2; pp. 155 - 196
Main Authors:	Eberhard, A. C., Luo, Y., Liu, S.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2019
Subjects:	Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical Secondary 58D15 Primary 59J52
Online Access:	Get full text
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Description
Summary:	Under the assumption of prox-regularity and the presence of a tilt stable local minimum we are able to show that a VU like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function.
ISSN:	0025-5610 1436-4646
DOI:	10.1007/s10107-018-1238-8