A GLOBALLY CONVERGENT PRIMAL-DUAL INTERIOR-POINT RELAXATION METHOD FOR NONLINEAR PROGRAMS

doi:10.1090/mcom/3487

	A GLOBALLY CONVERGENT PRIMAL-DUAL INTERIOR-POINT RELAXATION METHOD FOR NONLINEAR PROGRAMS
	Liu, Xin-Wei 1; Dai, Yu-Hong 2,3
刊名	MATHEMATICS OF COMPUTATION
	2020-05-01
卷号	89 期号:323 页码:1301-1329
关键词	Nonlinear programming constrained optimization interior-point method logarithmic barrier problem global convergence
ISSN号	0025-5718
DOI	10.1090/mcom/3487
英文摘要	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.
资助项目	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研究方向	Mathematics
语种	英语
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000550058300009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51798]
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.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
推荐引用方式 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.