DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
Optimization and Control
2018-09-13 v2 Data Structures and Algorithms
Machine Learning
Abstract
We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, second order cone, and semidefinite programming. This allows us to optimize over subsets of valid difference of convex decompositions (dcds) and find ones that speed up the convex-concave procedure (CCP). We prove, however, that optimizing over the entire set of dcds is NP-hard.
Cite
@article{arxiv.1510.01518,
title = {DC Decomposition of Nonconvex Polynomials with Algebraic Techniques},
author = {Amir Ali Ahmadi and Georgina Hall},
journal= {arXiv preprint arXiv:1510.01518},
year = {2018}
}