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On solving discontinuous extremal problems

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Abstract

An approach to solving discontinuous problems of optimization and control is described. The approach is based on the concept of approximate gradient introduced in Ref. 1. Generalizations of the theorems of Kuhn-Tucker and Dubovitsky-Milyutin and the maximum principle of Pontryagin are proved. The mathematical constructions described allow one to solve a wide variety of applied problems of optimization and control within the class of nonsmooth (including discontinuous) functions. The paper continues the investigations of Refs. 1–2.

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References

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Authors and Affiliations

  1. Department of Control and Optimization Theory, Chelyabinsk State University, Chelyabinsk, Russia

    V. D. Batukhtin (Rector of Chelyabinsk State University; Professor and Head)

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  1. V. D. Batukhtin
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Communicated by V. A. Troitskii

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Batukhtin, V.D. On solving discontinuous extremal problems. J Optim Theory Appl 77, 575–589 (1993). https://doi.org/10.1007/BF00940451

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