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A filter interior-point algorithm with projected Hessian updating for nonlinear optimization

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Abstract

Filter approaches, initially presented by Fletcher and Leyffer in 2002, are attractive methods for nonlinear programming. In this paper, we propose an interior-point barrier projected Hessian updating algorithm with line search filter method for nonlinear optimization. The Lagrangian function value instead of the objective function value is used in the filter. The damped BFGS updating is employed to maintain the positive definiteness of the matrices in projected Hessian updating algorithm. The numerical experiments are reported to show the effectiveness of the proposed algorithm.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Chao Gu

  2. Depart. of Math. and Statist., Shanghai LiXin University of Commerce, Shanghai, 201620, People’s Republic of China

    Chao Gu

  3. Business College, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Detong Zhu

Authors
  1. Chao Gu
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  2. Detong Zhu
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Correspondence to Chao Gu.

Additional information

The authors gratefully acknowledge the partial supports of the National Science Foundation Grant (10471094) of China, the Ph.D. Foundation Grant (0527003) of Chinese Education Ministry, the Shanghai Leading Academic Discipline Project (T0401), Shanghai LiXin University of Commerce (yh200817, 07KJYJ18) and the Science Foundation Grant (06YQ16, 05DZ11) of Shanghai Education Committee.

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Gu, C., Zhu, D. A filter interior-point algorithm with projected Hessian updating for nonlinear optimization. J. Appl. Math. Comput. 29, 67–80 (2009). https://doi.org/10.1007/s12190-008-0089-5

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  • DOI: https://doi.org/10.1007/s12190-008-0089-5

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