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Second-order necessary conditions in a domain optimization problem

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Abstract

Second-order necessary conditions of the Kuhn-Tucker type for optimality in a domain optimization problem are studied. The second variation, corresponding to a boundary variation, of the solution to a boundary-value problem is shown to exist and is given as the solution of a boundary-value problem of the same type. The boundary data are shown to be given in terms of the solution and the first variation of the solution. From these results, the second variation of the objective function is calculated to derive second-order necessary conditions of the Kuhn-Tucker type.

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Authors and Affiliations

  1. Department of Control Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

    N. Fujii (Associate Professor)

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  1. N. Fujii
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Additional information

Communicated by L. D. Berkovitz

A part of this work was presented under the title of “Second Variation and Its Application in a Domain Optimization Problem” at the 4th IFAC Symposium on Control of Distributed-Parameter Systems, Los Angeles, California, 1986 and appeared in the Proceedings of the Symposium, Control of Distributed Parameter Systems, Pergamon Press, 1986. The author wishes to express his thanks to Professor Y. Sakawa of Osaka University for his encouragement. The author thanks the referees for critical reading and helpful comments.

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Fujii, N. Second-order necessary conditions in a domain optimization problem. J Optim Theory Appl 65, 223–244 (1990). https://doi.org/10.1007/BF01102343

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