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Volume 20, Issue 3
Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems ㅡ Inequality Constrained Problems

Zi-You Gao, Tian-De Guo, Guo-Ping He & Fang Wu

J. Comp. Math., 20 (2002), pp. 301-312.

Published online: 2002-06

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  • Abstract

In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations gaving a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.

  • Keywords

Optimization, Inequality constraints, Algorithms, Sequential systems of linear equations, Coefficient matrices, Superlinear convergence.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-20-301, author = {Gao , Zi-YouGuo , Tian-DeHe , Guo-Ping and Wu , Fang}, title = {Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems ㅡ Inequality Constrained Problems}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {3}, pages = {301--312}, abstract = {

In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations gaving a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8919.html} }
TY - JOUR T1 - Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems ㅡ Inequality Constrained Problems AU - Gao , Zi-You AU - Guo , Tian-De AU - He , Guo-Ping AU - Wu , Fang JO - Journal of Computational Mathematics VL - 3 SP - 301 EP - 312 PY - 2002 DA - 2002/06 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8919.html KW - Optimization, Inequality constraints, Algorithms, Sequential systems of linear equations, Coefficient matrices, Superlinear convergence. AB -

In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations gaving a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.

Gao , Zi-YouGuo , Tian-DeHe , Guo-Ping and Wu , Fang. (2002). Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems ㅡ Inequality Constrained Problems. Journal of Computational Mathematics. 20 (3). 301-312. doi:
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