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DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
October 06, 2015 Β· Declared Dead Β· π Mathematical programming
"No code URL or promise found in abstract"
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Authors
Amir Ali Ahmadi, Georgina Hall
arXiv ID
1510.01518
Category
math.OC: Optimization & Control
Cross-listed
cs.DS,
stat.ML
Citations
47
Venue
Mathematical programming
Last Checked
6 months ago
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.
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