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On Unique Solutions of Multiple-State Optimal Design Problems on an Annulus

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  • Krešimir Burazin

    (University of Osijek)

Abstract

We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example.

Suggested Citation

  • Krešimir Burazin, 2018. "On Unique Solutions of Multiple-State Optimal Design Problems on an Annulus," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 329-344, May.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:2:d:10.1007_s10957-018-1284-7
    DOI: 10.1007/s10957-018-1284-7
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