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Nonconvex optimization using negative curvature within a modified linesearch

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  • Olivares, Alberto
  • Moguerza, Javier M.
  • Prieto, Francisco J.

Abstract

This paper describes a new algorithm for the solution of nonconvex unconstrained optimization problems, with the property of converging to points satisfying second-order necessary optimality conditions. The algorithm is based on a procedure which, from two descent directions, a Newton-type direction and a direction of negative curvature, selects in each iteration the linesearch model best adapted to the properties of these directions. The paper also presents results of numerical experiments that illustrate its practical efficiency.

Suggested Citation

  • Olivares, Alberto & Moguerza, Javier M. & Prieto, Francisco J., 2008. "Nonconvex optimization using negative curvature within a modified linesearch," European Journal of Operational Research, Elsevier, vol. 189(3), pages 706-722, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:706-722
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    References listed on IDEAS

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    1. Sun, Jie & Yang, Xiaoqi & Chen, Xiongda, 2005. "Quadratic cost flow and the conjugate gradient method," European Journal of Operational Research, Elsevier, vol. 164(1), pages 104-114, July.
    2. S. Sanmatías & E. Vercher, 1998. "A Generalized Conjugate Gradient Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 489-502, August.
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    Cited by:

    1. Javier Cano & Javier M. Moguerza & Francisco J. Prieto, 2017. "Using Improved Directions of Negative Curvature for the Solution of Bound-Constrained Nonconvex Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 474-499, August.
    2. Battauz, Michela & Vidoni, Paolo, 2022. "A likelihood-based boosting algorithm for factor analysis models with binary data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Alberto Olivares & Javier Moguerza, 2009. "Improving directions of negative curvature in an efficient manner," Annals of Operations Research, Springer, vol. 166(1), pages 183-201, February.

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    1. Javier Cano & Javier M. Moguerza & Francisco J. Prieto, 2017. "Using Improved Directions of Negative Curvature for the Solution of Bound-Constrained Nonconvex Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 474-499, August.
    2. Alberto Olivares & Javier Moguerza, 2009. "Improving directions of negative curvature in an efficient manner," Annals of Operations Research, Springer, vol. 166(1), pages 183-201, February.
    3. Shi, Zhen-Jun & Shen, Jie, 2007. "Convergence of Liu-Storey conjugate gradient method," European Journal of Operational Research, Elsevier, vol. 182(2), pages 552-560, October.

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