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 - <p style="text-align: justify;">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.</p>