A semidefinite programming method for integer convex quadratic minimization

被引：26

作者：

Park, Jaehyun ^{[1
]}

Boyd, Stephen ^{[2
]}

机构：

[1] Stanford Univ, Packard Bldg,Room 243,350 Serra Mall, Stanford, CA 94305 USA

[2] Stanford Univ, Packard Bldg,Room 254,350 Serra Mall, Stanford, CA 94305 USA

来源：

OPTIMIZATION LETTERS | 2018年 / 12卷 / 03期

关键词：

Convex optimization; Integer quadratic programming; Mixed-integer programming; Semidefinite relaxation; Branch-and-bound; ALGORITHMS; COMPLEXITY; LATTICE; MODELS;

D O I：

10.1007/s11590-017-1132-y

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the problem. By interpreting the solution to the SDP relaxation probabilistically, we obtain a randomized algorithm for finding good suboptimal solutions, and thus an upper bound on the optimal value. The effectiveness of the method is shown for numerical problem instances of various sizes.

引用

页码：499 / 518

页数：20

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