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DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
Amir Ali Ahmadi(a_a_a 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. Keywords: Difference of convex programming, conic relaxations, polynomial optimization, algebraic decomposition of polynomials Category 1: Linear, Cone and Semidefinite Programming Category 2: Global Optimization Category 3: Applications -- Science and Engineering (Statistics ) Citation: ORFE, Sherrerd Hall, Princeton University, Princeton, NJ 08540; October 2015 Download: [PDF] Entry Submitted: 10/09/2015 Modify/Update this entry | ||
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