123 citations · 525 across the 31 of their papers we have counts for
7 papers · 2 filters
Time-Varying Semidefinite Programs
Amir Ali Ahmadi, Bachir El Khadir
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data…
On the Complexity of Detecting Convexity over a Box
Amir Ali Ahmadi, Georgina Hall
It has recently been shown that the problem of testing global convexity of polynomials of degree four is {strongly} NP-hard, answering an open question of N.Z. Shor. This result is…
Robust-to-Dynamics Optimization
Amir Ali Ahmadi, Oktay Gunluk
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\right…
SOS-Convex Lyapunov Functions and Stability of Difference Inclusions
Amir Ali Ahmadi, Raphael M. Jungers
We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems).…
On the Complexity of Testing Attainment of the Optimal Value in Nonlinear Optimization
Amir Ali Ahmadi, Jeffrey Zhang
We prove that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can test whether the optimal value of a nonlinear optimization problem wh…
A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function
Amir Ali Ahmadi, Bachir El Khadir
We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an an…
On Algebraic Proofs of Stability for Homogeneous Vector Fields
Amir Ali Ahmadi, Bachir El Khadir
We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function which is the ratio of two polynomials (i.e., a…