593 citations · 1.9k across the 44 of their papers we have counts for
6 papers · 1 filter
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…
Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance
Aivar Sootla, Yang Zheng, Antonis Papachristodoulou
Diagonally dominant matrices have many applications in systems and control theory. Linear dynamical systems with scaled diagonally dominant drift matrices, which include stable pos…
Distributed Design for Decentralized Control using Chordal Decomposition and ADMM
Yang Zheng, Maryam Kamgarpour, Aivar Sootla +1
We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sp…
Fast ADMM for sum-of-squares programs using partial orthogonality
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property th…
Chordal decomposition in operator-splitting methods for sparse semidefinite programs
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou +2
We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive s…
Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programming using ADMM
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squa…