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Conditioning convex and nonconvex problems

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Abstract

Two ways of defining a well-conditioned minimization problem are introduced and related, with emphasis on the quantitative aspects. These concepts are used to study the behavior of the solution sets of minimization problems for functions with connected sublevel sets, generalizing results of Attouch-Wets in the convex case. Applications to continuity properties of subdifferentials and to projection mappings are pointed out.

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Authors and Affiliations

  1. Mathématiques URA 1204, Faculté des Sciences, Université de Pau, Pau, France

    J. -P. Penot (Professor)

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  1. J. -P. Penot
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Communicated by M. Avriel

We are grateful to M. Valadier for pointing out, during a lecture by the author in Montpellier in October 1990 presenting the main results of the present paper, that existence results in Section 2 of the present paper can be dissociated from estimates.

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Penot, J.P. Conditioning convex and nonconvex problems. J Optim Theory Appl 90, 535–554 (1996). https://doi.org/10.1007/BF02189795

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