Abstract

We put the emphasis on nonlinear (weak) sharp minimizers with respect to a gauge function. This concept plays an important role in both theoretical and numerical aspects of optimization. In the last part of the contribution we study the stability (in some appropriate sense) of local/global minimizers of an objective function f perturbed to f + g by a function g belonging to a suitable class of Lipschitz functions defined on metric spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Huynh Van Ngai

Department of Mathematics, University of Quynhon, Qui Nhon, Vietnam

ngaivn@yahoo.com

Keywords

  • Stability
  • slope
  • tilt stability
  • perturbations
  • sensitivity
  • varitional analysis

Mathematics Subject Classification

49J52, 90C30, 90C31

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Suggested citation

H. V. Ngai, M. Théra. “Nonlinear Sharp Minimum and the Stability of a Local Minimum on Metric Spaces.” Journal of Convex Analysis 31 (2024), No. 4, 1213–1226. https://doi.org/10.68381/jca31060

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.