Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5128369 | Operations Research Letters | 2017 | 6 Pages |
Abstract
We discuss two approaches to approximate the convex and concave envelopes of bilinear functions over hypercubes. The first approach is based on a semidefinite program. The second approach considers some predefined cover sets of a hypercube and leads to a linear program. Then we establish a connection between the convex envelope of a bilinear function and the concave envelope of a piecewise linear function. Numerical experiments are conducted to compare the two approaches. As an extension, a novel approach is discussed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Walid Ben-Ameur, Adam Ouorou, Guanglei Wang,