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LP/SDP Hierarchies and Sum of Squares Proofs 1Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Explains that nonnegativity checks reduce to semidefinite programming by writing a polynomial as a quadratic form over a chosen monomial basis and searching…
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LP/SDP Hierarchies and Sum of Squares Proofs 2Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Real infeasibility certificates appear as an f + g = -1 certificate with f in the ideal of equations and g in the cone generated by inequalities; bounding the…
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LP/SDP Hierarchies and Sum of Squares Proofs 3Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Part three shows an SOS/SDP proof that a triangle-free graph has at most asymptotically half the possible edges (an SOS version of Mantel’s theorem), by…
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LP/SDP Hierarchies and Sum of Squares Proofs 4Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Presents a concrete SOS-based algorithm: a quasi-polynomial time N^{O(log N / ε^2)} method that approximates the max of a degree‑4 polynomial (M defined as…
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Chordal Structure and Polynomial SystemsSolving Polynomial Equations (Simons Institute, 2014)2014-10-13
Proposes a chordal elimination algorithm that preserves sparsity by eliminating variables along a perfect elimination order, computes elimination ideals for…
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Semidefinite Hierarchies in Quantum InformationQuantum Games and Protocols2014-02-24
Semidefinite hierarchies convert hard nonnegativity and separability checks into tractable sum of squares and SDP feasibility problems by representing…
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