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Applying the pattern search implicit filtering algorithm for solving a noisy problem of parameter identification

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Abstract

Our contribution in this paper is twofold. First, the global convergence analysis of the recently proposed pattern search implicit filtering algorithm (PSIFA), aimed at linearly constrained noisy minimization problems, is revisited to address more general locally Lipschitz objective functions corrupted by noise. Second, PSIFA is applied for solving the damped harmonic oscillator parameter identification problem. This problem can be formulated as a linearly constrained optimization problem, for which the constraints are related to the features of the damping. Such a formulation rests upon a very expensive objective function whose evaluation comprises the numerical solution of an ordinary differential equation (ODE), with intrinsic numerical noise. Computational experimentation encompasses distinct choices for the ODE solvers, and a comparative analysis of the most effective options against the pattern search and the implicit filtering algorithms.

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Notes

  1. The matlab code is available at http://www4.ncsu.edu/~ctk/darts/imfil.m.

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Acknowledgements

We are thankful to professors Lúcio Tunes dos Santos (Institute of Mathematics, University of Campinas) and Pablo Siqueira Meirelles (Faculty of Mechanical Engineering, University of Campinas) for the discussions and valuable suggestions concerning the oscillator problem. We also thank the Associate Editor, professor Ernesto G. Birgin, and the anonymous reviewers, whose comments and remarks helped us to improve the presentation of our work. We are particularly indebted to the third referee, for pointing out fundamental corrections in the convergence analysis.

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  1. Institute of Mathematics, University of Campinas, Rua Sergio Buarque de Holanda, 651, Campinas, São Paulo, 13083-859, Brazil

    M. A. Diniz-Ehrhardt, D. G. Ferreira & S. A. Santos

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  1. M. A. Diniz-Ehrhardt
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  2. D. G. Ferreira
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  3. S. A. Santos
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Correspondence to S. A. Santos.

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Partially supported by Brazilian Funding Agencies Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP (Grants 2013/12964-4, 2013/07375-0, 2018/24293-0) and Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq (Grant 302915/2016-8). This paper is dedicated to professor J. M. Martínez on the occasion of his 70th birthday, with our great respect and admiration.

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Diniz-Ehrhardt, M.A., Ferreira, D.G. & Santos, S.A. Applying the pattern search implicit filtering algorithm for solving a noisy problem of parameter identification. Comput Optim Appl 76, 835–866 (2020). https://doi.org/10.1007/s10589-020-00182-2

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