123 citations · 525 across the 31 of their papers we have counts for
7 papers · 1 filter
Sum of squares certificates for stability of planar, homogeneous, and switched systems
Amir Ali Ahmadi, Pablo A. Parrilo
We show that existence of a global polynomial Lyapunov function for a homogeneous polynomial vector field or a planar polynomial vector field (under a mild condition) implies exist…
Response to "Counterexample to global convergence of DSOS and SDSOS hierarchies"
Amir Ali Ahmadi, Anirudha Majumdar
In a recent note [8], the author provides a counterexample to the global convergence of what his work refers to as "the DSOS and SDSOS hierarchies" for polynomial optimization prob…
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…
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…
Semidefinite Programming and Nash Equilibria in Bimatrix Games
Amir Ali Ahmadi, Jeffrey Zhang
We explore the power of semidefinite programming (SDP) for finding additive -approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic…
DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
Amir Ali Ahmadi, Anirudha Majumdar
In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite progra…
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…