ShanghaiTech University Knowledge Management System
| Global optimization in Hilbert space | |
| 2019-01 | |
| Source Publication | MATHEMATICAL PROGRAMMING
 |
| ISSN | 0025-5610 |
| Volume | 173Issue:1-2Pages:221-249 |
| Status | 已发表 |
| DOI | 10.1007/s10107-017-1215-7 |
| Abstract | We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an epsilon-suboptimal global solution within finite run-time for any given termination tolerance epsilon>0. Finally, we illustrate these results for a problem of calculus of variations. |
| Keyword | Infinite-dimensional optimization Complete search Branch-and-lift Convergence analysis Complexity analysis |
| Indexed By | SCI ; SCIE ; EI |
| Language | 英语 |
| Funding Project | Marie Curie Career Integration Grant[PCIG09-GA-2011-293953] |
| WOS Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000456970900007 |
| Publisher | SPRINGER HEIDELBERG |
| WOS Keyword | CONVEX COMPUTATION ; APPROXIMATIONS ; INTERSECTION ; INTEGRATION ; ELLIPSOIDS ; ALGORITHM ; CUT ; SET |
| Original Document Type | Article |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/29712 |
| Collection | 信息科学与技术学院_PI研究组_Boris Houska组 |
| Corresponding Author | Chachuat, Benoit |
| Affiliation | 1.ShanghaiTech Univ, Sch Informat Sci & Technol, 319 Yueyang Rd, Shanghai 200031, Peoples R China 2.Imperial Coll London, Ctr Proc Syst Engn, Dept Chem Engn, South Kensington Campus, London SW7 2AZ, England |
| First Author Affilication | School of Information Science and Technology |
| First Signature Affilication | School of Information Science and Technology |
| Recommended Citation GB/T 7714 | Houska, Boris,Chachuat, Benoit. Global optimization in Hilbert space[J]. MATHEMATICAL PROGRAMMING,2019,173(1-2):221-249. |
| APA | Houska, Boris,&Chachuat, Benoit.(2019).Global optimization in Hilbert space.MATHEMATICAL PROGRAMMING,173(1-2),221-249. |
| MLA | Houska, Boris,et al."Global optimization in Hilbert space".MATHEMATICAL PROGRAMMING 173.1-2(2019):221-249. |
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