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A PRIMAL-DUAL INTERIOR-POINT METHOD CAPABLE OF RAPIDLY DETECTING INFEASIBILITY FOR NONLINEAR PROGRAMS
Dai, Yu-Hong1; Liu, Xin-Wei2; Sun, Jie2,3,4
2020-03-01
Source PublicationJOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
ISSN1547-5816
Volume16Issue:2Pages:1009-1035
AbstractWith 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.
KeywordNonlinear programming constrained optimization infeasibility interior-point method global and local convergence
DOI10.3934/jimo.2018190
Indexed BySCI
Language英语
Funding ProjectChinese 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 Research AreaEngineering ; Operations Research & Management Science ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000514181500026
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50871
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLiu, Xin-Wei
Affiliation1.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
Recommended Citation
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.
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