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Parameter Identification for Nonlinear Abstract Cauchy Problems Using Quasilinearization

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Abstract

A quasilinearization approach to parameter identification in nonlinear abstract Cauchy problems in which the parameter appears in the nonlinear term, is presented. This approach has two main advantages over the classical one: it is much more intuitive and the derivation of the algorithm is done without need of the sensitivity equations on which classical quasilinearization is based. Sufficient conditions for the convergence of the algorithm are derived in terms of the regularity of the solutions with respect to the parameters. A comparison with the standard approach is presented and an application is included in which the nonphysical parameters in a mathematical model for shape memory alloys are estimated.

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Authors and Affiliations

  1. Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    T.L. Herdman (Professor)

  2. Instituto de Matemática Aplicada del Litoral (IMAL), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Santa Fe, Argentina

    P. Morin (Professor) & R.D. Spies

Authors
  1. T.L. Herdman
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  2. P. Morin
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  3. R.D. Spies
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Herdman, T., Morin, P. & Spies, R. Parameter Identification for Nonlinear Abstract Cauchy Problems Using Quasilinearization. Journal of Optimization Theory and Applications 113, 227–250 (2002). https://doi.org/10.1023/A:1014874707485

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  • DOI: https://doi.org/10.1023/A:1014874707485

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