SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs
成果类型：
Article
署名作者：
Nohra, Carlos J.; Raghunathan, Arvind U.; Sahinidis, Nikolaos, V
署名单位：
University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-021-01680-9
发表日期：
2022
页码：
203-233
关键词：
摘要：
We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of specialized solution algorithms. Our quadratic cuts are nonconvex, but define a convex feasible set when intersected with the equality constraints. We show that our relaxations are an outer-approximation of a semi-infinite convex program which under certain conditions is equivalent to a well-known semidefinite program relaxation. The new relaxations are implemented in the global optimization solver BARON, and tested by conducting numerical experiments on a large collection of problems. Results demonstrate that, for our test problems, these relaxations lead to a significant improvement in the performance of BARON.