KMS Of Academy of mathematics and systems sciences, CAS
| A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION | |
Liu, Xinwei1; Yuan, Yaxiang2
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| 2011 | |
| Source Publication | SIAM JOURNAL ON OPTIMIZATION
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| ISSN | 1052-6234 |
| Volume | 21Issue:2Pages:545-571 |
| Abstract | We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. First, we do not need to assume the boundedness of the iterative sequence. Second, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush-Kuhn-Tucker point, an approximate Fritz-John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the l 2 norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without requiring linear independence constraint qualification, the algorithm is shown to be locally superlinearly convergent. The preliminary numerical results show that the algorithm is robust and efficient when solving some small-and medium-sized problems from the CUTE collection. |
| Keyword | sequential quadratic programming penalty function filter regularity global and local convergence analysis |
| DOI | 10.1137/080739884 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[10971047] ; National Natural Science Foundation of China[10831006] ; Hebei Natural Science Foundation of China[A2010000011] ; CAS[kjcx-yw-s7] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000292247200006 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/12328 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Liu, Xinwei |
| Affiliation | 1.Hebei Univ Technol, Dept Appl Math, Tianjin 300401, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Liu, Xinwei,Yuan, Yaxiang. A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION[J]. SIAM JOURNAL ON OPTIMIZATION,2011,21(2):545-571. |
| APA | Liu, Xinwei,&Yuan, Yaxiang.(2011).A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION.SIAM JOURNAL ON OPTIMIZATION,21(2),545-571. |
| MLA | Liu, Xinwei,et al."A SEQUENTIAL QUADRATIC PROGRAMMING METHOD WITHOUT A PENALTY FUNCTION OR A FILTER FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION".SIAM JOURNAL ON OPTIMIZATION 21.2(2011):545-571. |
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