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Operations Research Transactions >

2015 , Vol. 19 >Issue 4: 48 - 58

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.04.005

A feasible sequential systems of linear equations algorithm for inequality constrained optimization

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  • 1.Yulin Normal University, Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin 53700, Guangxi, Chian

Received date: 2014-08-19

  Online published: 2015-12-15

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Abstract

In this paper, a feasible sequential systems of linear equations algorithm for inequality constrained optimization is proposed. At each iteration, the proposed algorithm solves only two systems of linear equations with a same coefficient matrix to obtain the feasible descent direction. Furthermore, the sparsity of the coefficient matrix is good. Under some necessary assumptions, the algorithm possesses global and strong convergence. Finally, some preliminary numerical
experiments are reported to show that the algorithm is effective.

Key words： inequality constrained optimization; sequential systems of linear equations algorithm; global convergence; strong convergence

Cite this article

MA Guodong, JIAN Jinbao . A feasible sequential systems of linear equations algorithm for inequality constrained optimization[J]. Operations Research Transactions, 2015 , 19(4) : 48 -58 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.04.005

References

 Han S P. Superlinearly convergence variable metric algorithm for general nonlinear programming problems [J].  Mathematical Programming,
 1976,11(1): 263-282.


 Facchinei F, Lucidi S. Quadraticly and superlinearly convergentm for the solution of inequality constrained optimization problem [J]. Journal of Optimization Theory and Applications, 1995,85(2):  265-289.

 Fletcher R, Leyffer S. Nonlinear programming without a penalty function [J]. Mathematical Programming, 2002,91(2): 239-269.

 Jian J B, Tang C M. An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity [J].Computers Mathematics with Applications, 2005,  49(2): 223-238.

 Zhu Z B. An efficient sequential quadratic programming algorithm for nonlinear programming [J]. Journal of Computational and Applied Mathematics,
2005,175(2): 447-464.

 Panier E R, Tits A L, Herskovits  J N. A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization [J]. SIAM Journal on Control and Optimization, 1988,  26(4):788-811.

 Qi H D, Qi L Q. A new QP-free, globally convergent, locally superlinearly  convergent algorithm for inequality constrained optimization [J].
 SIAM Journal on Optimization, 2000, 11(1): 113-132.

 Jian J B, Cheng W X. A superlinearly convergent strongly sub-feasible SSLE-type algorithm with working set for nonlinearly constrained optimization [J]. Journal of Computational and Applied Mathematics,2009, 225(1): 172-186.

Liu W A, Shen C G, Zhu X J, Pu D G. An infeasible QP-free algorithm without a penalty function or a filter for nonlinear inequality constrained optimization [J].  Optimization Methods Software, 2014, 29(6): 1238-1260.

 Mo X D, Jian J B, Yang S M. An improved strongly sub-feasible SSLE method for optimization problems and numerical experiments [J].  Appliedm Mathematics and Computation, 2011,  217: 7226-7237.

 Zhu Z B, Jian J B. An improved feasible QP-free algorithm for inequality constrained optimization [J].  Acta Mathematica Sinica, English Series, 2012,  28(12): 2475-2488.

Cheng W X, Huang C C, Jian J B. An improved infeasible SSLE method for constrained optimization without strict complementarity [J]. Computers  Operations Research, 2013,  40(5): 1506-1515.

 Jian J B, Han D L, Xu Q J. A fast convergent sequential linear equation method for inequality constrained optimization without strict complementarity [J].  Applied Mathematics and Computation, 2014, 236(1): 93-108.
  Ma G D, Jian J B. A QP-free algorithm of quasi-strongly sub-feasible  directions for inequality constrained optimization [J].  Journal  of Industrial and Management Optimization, 2015, 11(1): 307-328.

 简金宝. 光滑约束优化快速算法——理论分析与数值试验 [M]. 北京: 科学出版社, 2010.

 Hock W, Schittkowski K. Test examples for nonlinear programming codes [M]. Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, 1981.
Bongartz I, Conn A R, Gould N I, Toint P L. CUTE: Constrained and unconstrained testing environment [J]. Transactions on Mathematical Software ACM, 1995, 21 : 123-160.

 
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