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A Globally and Superlinearly Convergent Primal-dual Interior Point Method for General Constrained Optimization

Published online by Cambridge University Press:  05 August 2015

Jianling Li ,
Jian Lv  and
Jinbao Jian
Jianling Li
Affiliation:
College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China
Jian Lv
Affiliation:
School of Mathematics Science, Dalian University of Technology, Dalian, 116024, China
Jinbao Jian*
Affiliation:
School of Mathematics and Information Science, Yulin Normal University; Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin 537000, China
*
*Email addresses: jianlingli@126.com (J.L. Li), 710261120@qq.com (J. Lv), jianjb@gxu.edu.cn (J. B. Jian)
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Abstract

In this paper, a primal-dual interior point method is proposed for general constrained optimization, which incorporated a penalty function and a kind of new identification technique of the active set. At each iteration, the proposed algorithm only needs to solve two or three reduced systems of linear equations with the same coefficient matrix. The size of systems of linear equations can be decreased due to the introduction of the working set, which is an estimate of the active set. The penalty parameter is automatically updated and the uniformly positive definiteness condition on the Hessian approximation of the Lagrangian is relaxed. The proposed algorithm possesses global and superlinear convergence under some mild conditions. Finally, some preliminary numerical results are reported.

Keywords

general constrained optimizationprimal-dualactive setglobal convergencesuperlinear convergence.

MSC classification

Secondary: 65K05: Mathematical programming methods 90C30: Nonlinear programming 90C31: Sensitivity, stability, parametric optimization
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 3 , August 2015 , pp. 313 - 335
Copyright
Copyright © Global-Science Press 2015 

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