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An algorithm for nonlinear optimization using linear programming and equality constrained subproblems

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Abstract.

This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the ℓ1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program. The EQP incorporates a trust-region constraint and is solved (inexactly) by means of a projected conjugate gradient method. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEr [1, 15] test set.

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Authors and Affiliations

  1. Department of Computer Science, University of Colorado, Boulder, CO 80309, USA

    Richard H. Byrd

  2. Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0Qx, England, EU

    Nicholas I.M. Gould

  3. Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208-3118, USA

    Jorge Nocedal & Richard A. Waltz

Authors
  1. Richard H. Byrd
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  2. Nicholas I.M. Gould
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  3. Jorge Nocedal
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  4. Richard A. Waltz
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Corresponding author

Correspondence to Richard H. Byrd.

Additional information

This author was supported by Air Force Office of Scientific Research grant F49620-00-1-0162, Army Research Office Grant DAAG55-98-1-0176, and National Science Foundation grant INT-9726199.

This author was supported in part by the EPSRC grant GR/R46641.

These authors were supported by National Science Foundation grants CCR-9987818, ATM-0086579 and CCR-0219438 and Department of Energy grant DE-FG02-87ER25047-A004.

Report OTC 2002/4, Optimization Technology Center

To Roger Fletcher, with respect and admiration

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Byrd, R., Gould, N., Nocedal, J. et al. An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Math. Program., Ser. B 100, 27–48 (2003). https://doi.org/10.1007/s10107-003-0485-4

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  • DOI: https://doi.org/10.1007/s10107-003-0485-4

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