KMS Of Academy of mathematics and systems sciences, CAS
| Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting | |
| Jarre, Florian1; Lieder, Felix1; Liu, Ya-Feng2; Lu, Cheng3 | |
| 2020-04-01 | |
| Source Publication | JOURNAL OF GLOBAL OPTIMIZATION
 |
| ISSN | 0925-5001 |
| Volume | 76Issue:4Pages:913-932 |
| Abstract | This paper considers a generalization of the "max-cut-polytope" conv{xxT divide x is an element of Rn,|xk|=1for1 <= k <= n}in the space of real symmetric nxnmatrices with all-one diagonal to a complex "unit modulus lifting" conv{xx* divide x is an element of Cn,|xk|=1for1 <= k <= n}in the space of complex Hermitian nxn-matrices with all-one diagonal. The unit modulus lifting arises in applications such as digital communications and shares similar symmetry properties as the max-cut-polytope. Set-completely positive representations of both sets are derived and the relation of the complex unit modulus lifting to its semidefinite relaxation is investigated in dimensions 3 and 4. It is shown that the unit modulus lifting coincides with its semidefinite relaxation in dimension 3 but not in dimension 4. In dimension 4 a family of deep valid cuts for the unit modulus lifting is derived that could be used to strengthen the semidefinite relaxation. It turns out that the deep cuts are also implied by a second lifting that could be used alternatively. Numerical experiments are presented comparing the first lifting, the second lifting, and the unit modulus lifting for n=4. |
| Keyword | Max-cut problem Complex variables Semidefinite relaxation Unit modulus lifting |
| DOI | 10.1007/s10898-019-00813-x |
| Indexed By | SCI |
| Language | 英语 |
| WOS Research Area | Operations Research & Management Science ; Mathematics |
| WOS Subject | Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000520855000013 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50983 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Jarre, Florian |
| Affiliation | 1.Heinrich Heine Univ, Math Inst, Dusseldorf, Germany 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing, Peoples R China 3.North China Elect Power Univ, Sch Econ & Management, Beijing 102206, Peoples R China |
| Recommended Citation GB/T 7714 | Jarre, Florian,Lieder, Felix,Liu, Ya-Feng,et al. Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting[J]. JOURNAL OF GLOBAL OPTIMIZATION,2020,76(4):913-932. |
| APA | Jarre, Florian,Lieder, Felix,Liu, Ya-Feng,&Lu, Cheng.(2020).Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting.JOURNAL OF GLOBAL OPTIMIZATION,76(4),913-932. |
| MLA | Jarre, Florian,et al."Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting".JOURNAL OF GLOBAL OPTIMIZATION 76.4(2020):913-932. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment