123 citations · 525 across the 31 of their papers we have counts for
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Optimization over Structured Subsets of Positive Semidefinite Matrices via Column Generation
Amir Ali Ahmadi, Sanjeeb Dash, Georgina Hall
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear a…
Sum of Squares Basis Pursuit with Linear and Second Order Cone Programming
Amir Ali Ahmadi, Georgina Hall
We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SD…
DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
Amir Ali Ahmadi, Georgina Hall
We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, se…
Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
Amir Ali Ahmadi, Anirudha Majumdar
We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineer…
Lower Bounds on Complexity of Lyapunov Functions for Switched Linear Systems
Amir Ali Ahmadi, Raphael Jungers
We show that for any positive integer , there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary swi…