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On the Existence of Solutions of Two Optimization Problems

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  • Mariam Arabyan

    (Yerevan State University)

Abstract

In this paper, we prove the existence of solutions for the minimization problem of the shell weight for a given minimal frequency of the shell vibrations as well as for the maximization problem of the minimal frequency for a given shell weight. We consider an optimal control problem governed by an eigenvalue problem for a system of differential equations with variable coefficients. The form of the shell is considered as a control. Some of the coefficients are non-measurable. Earlier, we introduced certain special weighted functional spaces. By using these spaces, we establish the continuity of the considered minimal frequency functional and obtain the existence of solutions of both optimal control problems. At the end, we prove the Lipschitz continuity of the eigenvalue problem.

Suggested Citation

  • Mariam Arabyan, 2018. "On the Existence of Solutions of Two Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 291-305, May.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:2:d:10.1007_s10957-018-1266-9
    DOI: 10.1007/s10957-018-1266-9
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    References listed on IDEAS

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    1. Dean A. Carlson, 2015. "The Existence of Optimal Controls for Problems Defined on Time Scales," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 351-376, August.
    2. Y. He & B. Z. Guo, 2012. "The Existence of Optimal Solution for a Shape Optimization Problem on Starlike Domain," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 21-30, January.
    3. Alexander J. Zaslavski, 2013. "Nonconvex Optimal Control and Variational Problems," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-7378-7, September.
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