• Original Articles •

### NONLINEAR LAGRANGIANS FOR NONLINEAR PROGRAMMING BASED ON MODIFIED FISCHER-BURMEISTER NCP FUNCTIONS

Yonghong Ren1, Fangfang Guo2, Yang Li3

1. 1 School of Mathematics, Liaoning Normal University, Dalian, China;
2 School of Mathematics Sciences, Dalian University of Technology, Dalian, China;
3 School of Science, Dalian Nationalities University, Dalian, China
• Received:2014-08-26 Revised:2015-03-24 Online:2015-07-15 Published:2015-07-15
• Supported by:

The work of the first author was supported by the National Natural Science Foundation of China (11171138) and General Project of Scientific Research of the Education Department of Liaoning Province in 2015 (L2015291). The work of the third author was supported by the Fundamental Research Dalian Nationalities University (DC201502050406).

Yonghong Ren, Fangfang Guo, Yang Li. NONLINEAR LAGRANGIANS FOR NONLINEAR PROGRAMMING BASED ON MODIFIED FISCHER-BURMEISTER NCP FUNCTIONS[J]. Journal of Computational Mathematics, 2015, 33(4): 396-414.

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.

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