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An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point

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Abstract

For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using ε-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.

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Authors and Affiliations

  1. Northern Jiaotong University, 100044, Beijing, China

    Ziyou Gao

  2. Shandong Institute of Mining and Technology, 271019, Taian, China

    Guoping He

  3. Institute of Applied Mathematics, Chinese Academy of Sciences, 100080, Beijing, China

    Fang Wu

Authors
  1. Ziyou Gao
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  2. Guoping He
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  3. Fang Wu
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Additional information

Project partly supported by the National Natural Science Foundation of China and Tianyuan Foundation of China.

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Gao, Z., He, G. & Wu, F. An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point. Sci. China Ser. A-Math. 40, 561–571 (1997). https://doi.org/10.1007/BF02876059

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  • DOI: https://doi.org/10.1007/BF02876059

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