KMS Of Academy of mathematics and systems sciences, CAS
| A GLOBALLY CONVERGENT PRIMAL-DUAL INTERIOR-POINT RELAXATION METHOD FOR NONLINEAR PROGRAMS | |
| Liu, Xin-Wei1; Dai, Yu-Hong2,3 | |
| 2020-05-01 | |
| Source Publication | MATHEMATICS OF COMPUTATION
 |
| ISSN | 0025-5718 |
| Volume | 89Issue:323Pages:1301-1329 |
| Abstract | We prove that the classic logarithmic barrier problem is equivalent to a particular logarithmic barrier positive relaxation problem with barrier and scaling parameters. Based on the equivalence, a line-search primal-dual interior-point relaxation method for nonlinear programs is presented. Our method does not require any primal or dual iterates to be interior-points, which has similarity to some warmstarting interior-point methods and is different from most of the globally convergent interior-point methods in the literature. A new logarithmic barrier penalty function dependent on both primal and dual variables is used to prompt the global convergence of the method, where the penalty parameter is adaptively updated. Without assuming any regularity condition, it is proved that our method will either terminate at an approximate KKT point of the original problem, an approximate infeasible stationary point, or an approximate singular stationary point of the original problem. Some preliminary numerical results are reported, including the results for a well-posed problem for which many line-search interior-point methods were demonstrated not to be globally convergent, a feasible problem for which the LICQ and the MFCQ fail to hold at the solution and an infeasible problem, and for some standard test problems of the CUTE collection. Correspondingly, for comparison we also report the numerical results obtained by the interior-point solver IPOPT. These results show that our algorithm is not only efficient for well-posed feasible problems, but is also applicable for some feasible problems without LICQ or MFCQ and some infeasible problems. |
| Keyword | Nonlinear programming constrained optimization interior-point method logarithmic barrier problem global convergence |
| DOI | 10.1090/mcom/3487 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Chinese NSF[11631013] ; Chinese NSF[11331012] ; Chinese NSF[81173633] ; Chinese NSF[11671116] ; Chinese NSF[11271107] ; Major Research Plan of the National Natural Science Foundation of China[91630202] ; Hebei Natural Science Foundation of China[A2015202365] ; National Key Basic Research Program of China[2015CB856000] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000550058300009 |
| Publisher | AMER MATHEMATICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51799 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Xin-Wei |
| Affiliation | 1.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Liu, Xin-Wei,Dai, Yu-Hong. A GLOBALLY CONVERGENT PRIMAL-DUAL INTERIOR-POINT RELAXATION METHOD FOR NONLINEAR PROGRAMS[J]. MATHEMATICS OF COMPUTATION,2020,89(323):1301-1329. |
| APA | Liu, Xin-Wei,&Dai, Yu-Hong.(2020).A GLOBALLY CONVERGENT PRIMAL-DUAL INTERIOR-POINT RELAXATION METHOD FOR NONLINEAR PROGRAMS.MATHEMATICS OF COMPUTATION,89(323),1301-1329. |
| MLA | Liu, Xin-Wei,et al."A GLOBALLY CONVERGENT PRIMAL-DUAL INTERIOR-POINT RELAXATION METHOD FOR NONLINEAR PROGRAMS".MATHEMATICS OF COMPUTATION 89.323(2020):1301-1329. |
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