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Nichtlineare Optimierung mit unendlich vielen Nebenbedingungen

Nonlinear programming with infinitely many constraints

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Zusammenfassung

Es wird das Problem betrachtet, einFréchet-differenzierbares Funktional auf einer Teilmenge eines normierten Verktorraumes unter endlich oder unendlich vielenFréchet-differenzierbaren Nebenbedingungen zum Minimum zu machen. Unter Heranziehung von Tangentialkegeln und linearisierenden Kegeln werden notwendige und hinreichende Bedingungen für Lösungen des Problems und insbesondere eine Multiplikatorenregel angegeben.

Summary

We consider the problem of minimizing aFréchet differentiable functional on a subset of a normed linear space under finitely or infinitely manyFréchet differentiable constraints. Using tangent cones and linearizing cones we derive necessary and sufficient conditions for solutions of the problem. In particular a multiplier rule is obtained.

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Literatur

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Author information

Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik der RWTH Aachen, Templergraben 55, BRD-51, Aachen, Deutschland

    Werner Krabs

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  1. Werner Krabs
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Krabs, W. Nichtlineare Optimierung mit unendlich vielen Nebenbedingungen. Computing 7, 204–214 (1971). https://doi.org/10.1007/BF02242347

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  • DOI: https://doi.org/10.1007/BF02242347