Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization

doi:10.1007/s10589-014-9675-7

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	Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization
	Shen, Chungen 1; Zhang, Lei-Hong 2; Wang, Bo 3; Shao, Wenqiong 4
刊名	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
	2014-12
卷号	59 期号:3 页码:435-473
关键词	Sequential quadratic programming method Non-monotonicity Convergence analysis RCPLD Strict MFCQ
ISSN号	0926-6003
DOI	10.1007/s10589-014-9675-7
英文摘要	In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277-303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian-Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush-Kuhn-Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method.
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000344803000003
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/1661]
专题	上海财经大学
通讯作者	Shen, Chungen
作者单位	1.Shanghai Finance Univ, Dept Appl Math, Shanghai 201209, Peoples R China; 2.Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China; 3.Nanjing Univ Finance & Econ, Sch Appl Math, Shanghai 200092, Peoples R China; 4.Wayne State Univ, Ind & Syst Engn Dept, Detroit, MI 48202 USA
推荐引用方式 GB/T 7714	Shen, Chungen,Zhang, Lei-Hong,Wang, Bo,et al. Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2014,59(3):435-473.
APA	Shen, Chungen,Zhang, Lei-Hong,Wang, Bo,&Shao, Wenqiong.(2014).Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,59(3),435-473.
MLA	Shen, Chungen,et al."Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 59.3(2014):435-473.