کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5128274 1489491 2017 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Binary quadratic optimization problems that are difficult to solve by conic relaxations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات کنترل و بهینه سازی
پیش نمایش صفحه اول مقاله
Binary quadratic optimization problems that are difficult to solve by conic relaxations
چکیده انگلیسی

We study conic relaxations including semidefinite programming (SDP) relaxations and doubly nonnegative programming (DNN) relaxations to find the optimal values of binary QOPs. The main focus of the study is on how the relaxations perform with respect to the rank of the coefficient matrix in the objective of a binary QOP. More precisely, for a class of binary QOP instances, which include the max-cut problem of a graph with an odd number of nodes and equal weight, we show numerically that (1) neither the standard DNN relaxation nor the DNN relaxation derived from the completely positive formulation by Burer performs better than the standard SDP relaxation, and (2) Lasserre's hierarchy of SDP relaxations requires solving the SDP with the relaxation order at least ⌈n/2⌉ to attain the optimal value. The bound ⌈n/2⌉ for the max-cut problem of a graph with equal weight is consistent with Laurent's conjecture in 2003, which was proved recently by Fawzi, Saunderson and Parrilo in 2015.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Optimization - Volume 24, May 2017, Pages 170-183
نویسندگان
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