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Quantitative stability of variational systems: III.ε-approximate solutions (1993)

Attouch, Hedy ; Wets, Roger J. -B.

Springer

Mathematical programming 61 (1993), S. 197-214

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ISSN: 1436-4646

Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01582147

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