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Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints

Author

Listed:
  • Z. Y. Gao

    (Northern Jiaotong University)

  • G. P. He

    (Academia Sinica)

  • F. Wu

    (Academia Sinica)

Abstract

In Ref. 1, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints was proposed. At each iteration, this new algorithm only needs to solve four systems of linear equations having the same coefficient matrix, which is much less than the amount of computation required for existing SQP algorithms. Moreover, unlike the quadratic programming subproblems of the SQP algorithms (which may not have a solution), the subproblems of the SSLE algorithm are always solvable. In Ref. 2, it is shown that the new algorithm can also be used to deal with nonlinear optimization problems having both equality and inequality constraints, by solving an auxiliary problem. But the algorithm of Ref. 2 has to perform a pivoting operation to adjust the penalty parameter per iteration. In this paper, we improve the work of Ref. 2 and present a new algorithm of sequential systems of linear equations for general nonlinear optimization problems. This new algorithm preserves the advantages of the SSLE algorithms, while at the same time overcoming the aforementioned shortcomings. Some numerical results are also reported.

Suggested Citation

  • Z. Y. Gao & G. P. He & F. Wu, 1997. "Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 371-397, November.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:2:d:10.1023_a:1022639306130
    DOI: 10.1023/A:1022639306130
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    Cited by:

    1. Jian, Jin-Bao & Pan, Hua-Qin & Tang, Chun-Ming & Li, Jian-Ling, 2015. "A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 560-578.

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