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math.OC2017★ 2 cited
Improving Efficiency and Scalability of Sum of Squares Optimization: Recent Advances and Limitations
Amir Ali Ahmadi, Georgina Hall, Antonis Papachristodoulou +2
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for…
math.OC2017
On the construction of converging hierarchies for polynomial optimization based on certificates of global positivity
Amir Ali Ahmadi, Georgina Hall
In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much…
math.OC2017
Polynomial Norms
Amir Ali Ahmadi, Etienne de Klerk, Georgina Hall
In this paper, we study polynomial norms, i.e. norms that are the root of a degree- homogeneous polynomial . We first show that a necessary and sufficient con…