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Adaptive Algorithm for Constrained Least-Squares Problems

Author

Listed:
  • Z.F. Li

    (Australian National University)

  • M.R. Osborne

    (Australian National University)

  • T. Prvan

    (University of Canberra)

Abstract

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:2:d:10.1023_a:1016043919978
    DOI: 10.1023/A:1016043919978
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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. 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.

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