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Volume 33, Issue 4
Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions

Yonghong Ren, Fangfang Guo & Yang Li

DOI: 10.4208/jcm.1503-m2014-0044

J. Comp. Math., 33 (2015), pp. 396-414.

Published online: 2015-08

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  • Abstract

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.

  • Keywords

nonlinear Lagrangian, nonlinear Programming, modified Fischer-Burmeister NCP function, dual algorithm, condition number.

  • AMS Subject Headings

90C30, 49M37, 65K05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ryhong@lnnu.edu.cn (Yonghong Ren)

gracewuo@163.com (Fangfang Guo)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-396, author = {Ren , YonghongGuo , Fangfang and Li , Yang}, title = {Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {4}, pages = {396--414}, abstract = {

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1503-m2014-0044}, url = {http://global-sci.org/intro/article_detail/jcm/9850.html} }
TY - JOUR T1 - Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions AU - Ren , Yonghong AU - Guo , Fangfang AU - Li , Yang JO - Journal of Computational Mathematics VL - 4 SP - 396 EP - 414 PY - 2015 DA - 2015/08 SN - 33 DO - http://doi.org/10.4208/jcm.1503-m2014-0044 UR - https://global-sci.org/intro/article_detail/jcm/9850.html KW - nonlinear Lagrangian, nonlinear Programming, modified Fischer-Burmeister NCP function, dual algorithm, condition number. AB -

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.

Ren , YonghongGuo , Fangfang and Li , Yang. (2015). Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions. Journal of Computational Mathematics. 33 (4). 396-414. doi:10.4208/jcm.1503-m2014-0044
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