KMS Of Academy of mathematics and systems sciences, CAS
| 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 Publication | JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
 |
| ISSN | 1547-5816 |
| Volume | 16Issue:2Pages:1009-1035 |
| Abstract | 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. |
| Keyword | Nonlinear programming constrained optimization infeasibility interior-point method global and local convergence |
| DOI | 10.3934/jimo.2018190 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Engineering ; Operations Research & Management Science ; Mathematics |
| WOS Subject | Engineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications |
| WOS ID | WOS:000514181500026 |
| Publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50871 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Xin-Wei |
| Affiliation | 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 |
| 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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