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A nonmonotone line search filter method with reduced Hessian updating for nonlinear optimization

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Abstract

This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization. In order to deal with large scale problems, a reduced Hessian matrix is approximated by BFGS updates. The new method assures global convergence without using a merit function. By Lagrangian function in the filter and nonmonotone scheme, the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved. The primary numerical experiments are reported to show effectiveness of the proposed algorithm.

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Authors and Affiliations

  1. School of Mathematics and Informatics, Shanghai Lixin University of Commerce, Shanghai, 201620, China

    Chao Gu

  2. Business College, Shanghai Normal University, Shanghai, 200234, China

    Detong Zhu

Authors
  1. Chao Gu
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  2. Detong Zhu
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Corresponding author

Correspondence to Chao Gu.

Additional information

This research was supported by the National Science Foundation of China under Grant No. 10871130, the Ph.D Foundation under Grant No. 20093127110005, the Shanghai Leading Academic Discipline Project under Grant No. S30405, and the Innovation Program of Shanghai Municipal Education Commission under Grant No. 12YZ174.

This paper was recommended for publication by Editor WANG Shouyang.

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Gu, C., Zhu, D. A nonmonotone line search filter method with reduced Hessian updating for nonlinear optimization. J Syst Sci Complex 26, 534–555 (2013). https://doi.org/10.1007/s11424-012-0036-2

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  • DOI: https://doi.org/10.1007/s11424-012-0036-2

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