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Metrically well-set minimization problems

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Abstract

A concept of well-posedness, or more exactly of stability in a metric sense, is introduced for minimization problems on metric spaces generalizing the notion due to Tykhonov to situations in which there is no uniqueness of solutions. It is compared with other concepts, in particular to a variant of the notion after Hadamard reformulated via a metric semicontinuity approach. Concrete criteria of well-posedness are presented, e.g., for convex minimization problems.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Ewa Bednarczuk

  2. Faculte des Sciences, Universite de Pau, Av. de l'Universite, 64000, Pau, France

    Jean-Paul Penot

Authors
  1. Ewa Bednarczuk
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  2. Jean-Paul Penot
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Communicated by I. Lasiecka

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Bednarczuk, E., Penot, JP. Metrically well-set minimization problems. Appl Math Optim 26, 273–285 (1992). https://doi.org/10.1007/BF01371085

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  • DOI: https://doi.org/10.1007/BF01371085

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