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Indexed by:期刊论文

Date of Publication:2015-01-01

Journal:JOURNAL OF COMPUTATIONAL MATHEMATICS

Included Journals:SCIE、Scopus

Volume:33

Issue:4

Page Number:396-414

ISSN No.:0254-9409

Key Words:nonlinear Lagrangian; nonlinear Programming; modified Fischer-Burmeister NCP function; dual algorithm; condition number

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.