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.
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Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.
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Attouch, H., Wets, R.J.B. Quantitative stability of variational systems: III.ε-approximate solutions. Mathematical Programming 61, 197–214 (1993). https://doi.org/10.1007/BF01582147
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DOI: https://doi.org/10.1007/BF01582147