A non-monotone line search multidimensional filter-SQP method for general nonlinear programming

In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wächter–Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with...

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Published in:	Numerical algorithms Vol. 56; no. 4; pp. 537 - 559
Main Authors:	Gu, Chao, Zhu, Detong
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01.04.2011 Springer Nature B.V
Subjects:	Algebra Algorithms Computer Science Constraints Convergence Mathematical models Nonlinear programming Nonlinearity Numeric Computing Numerical Analysis Original Paper Programming Searching Theory of Computation Line search General nonlinear programming 65K05 90C30 90C55 Multidimensional filter Maratos effect 49M37 Non-monotone Convergence
ISSN:	1017-1398, 1572-9265
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Abstract	In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wächter–Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with the non-monotone technique and second order correction step, it is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved. Numerical results show that the new approach is efficient.
AbstractList	In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wächter–Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with the non-monotone technique and second order correction step, it is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved. Numerical results show that the new approach is efficient. In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wachter--Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with the non-monotone technique and second order correction step, it is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved. Numerical results show that the new approach is efficient.
Author	Gu, Chao Zhu, Detong
Author_xml	– sequence: 1 givenname: Chao surname: Gu fullname: Gu, Chao email: chaogumath@gmail.com organization: School of Math. and Info., Shanghai LiXin University of Commerce – sequence: 2 givenname: Detong surname: Zhu fullname: Zhu, Detong organization: Business College, Shanghai Normal University
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Cites_doi	10.1007/b98874 10.1007/s101070100263 10.1016/j.camwa.2008.05.030 10.1137/040603851 10.1007/s10496-008-0055-y 10.1137/S1052623403422637 10.1137/S0036144504446096 10.1137/S105262340038081X 10.1007/s12190-008-0089-5 10.1007/s101070100244 10.1137/0728063 10.1137/S1052623499357258 10.1016/j.apnum.2008.01.005 10.1007/s10107-002-0343-9 10.1137/0723046 10.1137/S1052623403426544 10.1090/conm/163/01559 10.1007/978-3-642-48320-2
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