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A linear programming-based optimization algorithm for solving nonlinear programming problems

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  • Still, Claus
  • Westerlund, Tapio

Abstract

In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.

Suggested Citation

  • Still, Claus & Westerlund, Tapio, 2010. "A linear programming-based optimization algorithm for solving nonlinear programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 658-670, February.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:658-670
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    References listed on IDEAS

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    1. Still, Claus & Westerlund, Tapio, 2006. "A sequential cutting plane algorithm for solving convex NLP problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 444-464, September.
    2. R. E. Griffith & R. A. Stewart, 1961. "A Nonlinear Programming Technique for the Optimization of Continuous Processing Systems," Management Science, INFORMS, vol. 7(4), pages 379-392, July.
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    Cited by:

    1. Trindade, Graça & Ambrósio, Jorge, 2012. "An optimization method to estimate models with store-level data: A case study," European Journal of Operational Research, Elsevier, vol. 217(3), pages 664-672.

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