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A hybrid global optimization algorithm for non-linear least squares regression

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  • Antanas Žilinskas
  • Julius Žilinskas

Abstract

A hybrid global optimization algorithm is proposed aimed at the class of objective functions with properties typical of the problems of non-linear least squares regression. Three components of hybridization are considered: simplicial partition of the feasible region, indicating and excluding vicinities of the main local minimizers from global search, and computing the indicated local minima by means of an efficient local descent algorithm. The performance of the algorithm is tested using a collection of non-linear least squares problems evaluated by other authors as difficult global optimization problems. Copyright Springer Science+Business Media, LLC. 2013

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  • Antanas Žilinskas & Julius Žilinskas, 2013. "A hybrid global optimization algorithm for non-linear least squares regression," Journal of Global Optimization, Springer, vol. 56(2), pages 265-277, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:265-277
    DOI: 10.1007/s10898-011-9840-9
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    References listed on IDEAS

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    1. Tvrdik, Josef & Krivy, Ivan & Misik, Ladislav, 2007. "Adaptive population-based search: Application to estimation of nonlinear regression parameters," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 713-724, October.
    2. Demidenko, Eugene, 2006. "Criteria for global minimum of sum of squares in nonlinear regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1739-1753, December.
    3. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    4. Antanas Žilinskas & Julius Žilinskas, 2010. "P-algorithm based on a simplicial statistical model of multimodal functions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 396-412, December.
    5. Dorsey, Robert E & Mayer, Walter J, 1995. "Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability, and Other Irregular Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 53-66, January.
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    Cited by:

    1. Usama Khaled & Ali M. Eltamaly & Abderrahmane Beroual, 2017. "Optimal Power Flow Using Particle Swarm Optimization of Renewable Hybrid Distributed Generation," Energies, MDPI, vol. 10(7), pages 1-14, July.
    2. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    3. Daniela Lera & Yaroslav D. Sergeyev, 2018. "GOSH: derivative-free global optimization using multi-dimensional space-filling curves," Journal of Global Optimization, Springer, vol. 71(1), pages 193-211, May.
    4. Christopher M. Cotnoir & Balša Terzić, 2017. "Decoupling linear and nonlinear regimes: an evaluation of efficiency for nonlinear multidimensional optimization," Journal of Global Optimization, Springer, vol. 68(3), pages 663-675, July.
    5. James Calvin & Gražina Gimbutienė & William O. Phillips & Antanas Žilinskas, 2018. "On convergence rate of a rectangular partition based global optimization algorithm," Journal of Global Optimization, Springer, vol. 71(1), pages 165-191, May.
    6. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
    7. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.

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