A nonlinear Lagrangian based on Fischer-Burmeister NCP function

This paper proposes a nonlinear Lagrangian Based on Fischer-Burmeister NCP function 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...

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Vydáno v:Applied mathematics and computation Ročník 188; číslo 2; s. 1344 - 1363
Hlavní autoři: Ren, Yong-Hong, Zhang, Li-Wei, Xiao, Xian-Tao
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Elsevier Inc 15.05.2007
Elsevier
Témata:
Augmented Lagrangian
Calculus of variations and optimal control
Condition number
Dual algorithm
Dual function
Exact sciences and technology
Fischer-Burmeister NCP function
Mathematical analysis
Mathematics
Nonlinear Lagrangian
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Special functions
Condition number
Nonlinear Lagrangian
Fischer-Burmeister NCP function
Dual function
Dual algorithm
Augmented Lagrangian
Lagrangian
Optimization method
Duality
Nonlinear problems
Non linear programming
Algorithm
Penalty method
Bounded solution
Convergence
Constrained optimization
Numerical analysis
Applied mathematics
Optimal solution
Inequality constraint
Problem solving
ISSN:0096-3003, 1873-5649
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Shrnutí:This paper proposes a nonlinear Lagrangian Based on Fischer-Burmeister NCP function 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. Moreover, the paper develops the dual approach associated with the proposed nonlinear Lagrangian, in which the related duality theorem is demonstrated. Furthermore, it is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Numerical results for solving several nonlinear programming problems are reported, showing that the new nonlinear Lagrangian is superior over other known nonlinear Lagrangians for solving some nonlinear programming problems.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.10.084