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- Amir Ali Ahmadi, Alexander Olshevsky, Pablo A. Parrilo, John N. Tsitsiklis
- Math. Program.
- 2013

We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) isâ€¦ (More)

- Amir Ali Ahmadi, Pablo A. Parrilo
- 2008 47th IEEE Conference on Decision and Control
- 2008

We relax the monotonicity requirement of LyapunovÂ¿s theorem to enlarge the class of functions that can provide certificates of stability. To this end, we propose two new sufficient conditions forâ€¦ (More)

- Amir Ali Ahmadi, Pablo A. Parrilo
- Math. Program.
- 2012

<lb>A multivariate polynomial p(x) = p(x1, . . . , xn) is sos-convex if its Hessian H(x) can be<lb>factored as H(x) = M (x)M(x) with a possibly nonsquare polynomial matrix M(x). It is<lb>easy to seeâ€¦ (More)

- Amir Ali Ahmadi, RaphaÃ«l M. Jungers, Pablo A. Parrilo, Mardavij Roozbehani
- SIAM J. Control and Optimization
- 2014

We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system viaâ€¦ (More)

- Amir Ali Ahmadi, Anirudha Majumdar
- 2014 48th Annual Conference on Informationâ€¦
- 2014

Sum of squares (SOS) optimization has been a powerful and influential addition to the theory of optimization in the past decade. Its reliance on relatively large-scale semidefinite programming,â€¦ (More)

- Amir Ali Ahmadi
- ArXiv
- 2011

The contributions of the first half of this thesis are on the computational and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial timeâ€¦ (More)

- Amir Ali Ahmadi, Miroslav Krstic, Pablo A. Parrilo
- IEEE Conference on Decision and Control andâ€¦
- 2011

We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.

- Amir Ali Ahmadi, Pablo A. Parrilo
- SIAM Journal on Optimization
- 2013

Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials via the definition of convexity, its first orderâ€¦ (More)

- Amir Ali Ahmadi, Pablo A. Parrilo
- IEEE Conference on Decision and Control andâ€¦
- 2011

Despite the pervasiveness of sum of squares (sos) techniques in Lyapunov analysis of dynamical systems, the converse question of whether sos Lyapunov functions exist whenever polynomial Lyapunovâ€¦ (More)

- Amir Ali Ahmadi, Sanjeeb Dash, Georgina Hall
- Discrete Optimization
- 2017

We develop algorithms to construct inner approximations of the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linearâ€¦ (More)