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Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares

Author

Listed:
  • Narges Bidabadi

    (Yazd University)

  • Nezam Mahdavi-Amiri

    (Sharif University of Technology)

Abstract

We present a superlinearly convergent exact penalty method for solving constrained nonlinear least squares problems, in which the projected exact penalty Hessian is approximated by using a structured secant updating scheme. We give general conditions for the two-step superlinear convergence of the algorithm and prove that the projected structured Broyden–Fletcher–Goldfarb–Shanno (BFGS), Powell-symmetric-Broyden (PSB), and Davidon–Fletcher–Powell (DFP) update formulas satisfy these conditions. Then we extend the results to the projected structured convex Broyden family update formulas. Extensive testing results obtained by an implementation of our algorithms, as compared to the results obtained by several other competent algorithms, demonstrate the efficiency and robustness of the proposed approach.

Suggested Citation

  • Narges Bidabadi & Nezam Mahdavi-Amiri, 2014. "Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 154-190, July.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0438-x
    DOI: 10.1007/s10957-013-0438-x
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    References listed on IDEAS

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    1. Wei Xu & Thomas Coleman & Gang Liu, 2012. "A secant method for nonlinear least-squares minimization," Computational Optimization and Applications, Springer, vol. 51(1), pages 159-173, January.
    2. Z.F. Li & M.R. Osborne & T. Prvan, 2002. "Adaptive Algorithm for Constrained Least-Squares Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 423-441, August.
    3. M. Fernanda & P. Costa & Edite Fernandes, 2005. "A primal-dual interior-point algorithm for nonlinear least squares constrained problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 145-166, June.
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    Cited by:

    1. Dominique Orban & Abel Soares Siqueira, 2020. "A regularization method for constrained nonlinear least squares," Computational Optimization and Applications, Springer, vol. 76(3), pages 961-989, July.
    2. Hui-Ping Cao & Dong-Hui Li, 2017. "Partitioned quasi-Newton methods for sparse nonlinear equations," Computational Optimization and Applications, Springer, vol. 66(3), pages 481-505, April.

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