A PRIMAL-DUAL INTERIOR-POINT METHOD CAPABLE OF RAPIDLY DETECTING INFEASIBILITY FOR NONLINEAR PROGRAMS

doi:10.3934/jimo.2018190

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	A PRIMAL-DUAL INTERIOR-POINT METHOD CAPABLE OF RAPIDLY DETECTING INFEASIBILITY FOR NONLINEAR PROGRAMS
	Dai, Yu-Hong 1; Liu, Xin-Wei 2; Sun, Jie 2,3,4
	2020-03-01
发表期刊	JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
ISSN	1547-5816
卷号	16 期号:2 页码:1009-1035
摘要	With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is efficient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature.
关键词	Nonlinear programming constrained optimization infeasibility interior-point method global and local convergence
DOI	10.3934/jimo.2018190
收录类别	SCI
语种	英语
资助项目	Chinese NSF[11631013] ; Chinese NSF[11331012] ; Chinese NSF[81173633] ; Chinese NSF[11671116] ; Chinese NSF[11271107] ; National Key Basic Research Program of China[2015CB856000] ; Major Research Plan of the NSFC[91630202] ; Australia Research Council[DP-160101819]
WOS研究方向	Engineering ; Operations Research & Management Science ; Mathematics
WOS类目	Engineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000514181500026
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50871
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Xin-Wei
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China 3.Curtin Univ, Sch Sci, Perth, WA, Australia 4.Natl Univ Singapore, Sch Business, Singapore, Singapore
推荐引用方式 GB/T 7714	Dai, Yu-Hong,Liu, Xin-Wei,Sun, Jie. A PRIMAL-DUAL INTERIOR-POINT METHOD CAPABLE OF RAPIDLY DETECTING INFEASIBILITY FOR NONLINEAR PROGRAMS[J]. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2020,16(2):1009-1035.
APA	Dai, Yu-Hong,Liu, Xin-Wei,&Sun, Jie.(2020).A PRIMAL-DUAL INTERIOR-POINT METHOD CAPABLE OF RAPIDLY DETECTING INFEASIBILITY FOR NONLINEAR PROGRAMS.JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,16(2),1009-1035.
MLA	Dai, Yu-Hong,et al."A PRIMAL-DUAL INTERIOR-POINT METHOD CAPABLE OF RAPIDLY DETECTING INFEASIBILITY FOR NONLINEAR PROGRAMS".JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 16.2(2020):1009-1035.