### Summary

## SOFTWARE

I contribute to the open-source software projects described below.

Code accompanying some of my publications is available on the aeroimperial-optimization GitHub page.

## QUINOPT

QUINOPT (QUadratic INtegral OPTimisation) is an open-source add-on for the MATLAB optimisation modelling toolbox YALMIP, aimed at the computation of rigorous upper and lower bounds on the optimal value of optimisation problems with infinite-dimensional polynomial quadratic integral inequality constraints. Such problems commonly arise from stability analysis of linear partial differential equations using the so-called *energy method* (also known as L^{2} stability), and when bounding time-averaged properties of turbulent fluid flows using the so-called *background method*.

**Collaborators:** Andrew Wynn (Imperial College London), Antonis Papachristodoulou (University of Oxford), Paul Goulart (University of Oxford).

## AEROIMPERIAL-YALMIP

Aeroimperial-yalmip is a fork of the MATLAB optimization toolbox YALMIP with a series of useful additional features, such as:

1) Support for the multiple-precision SDP solver SDPA-GMP

2) Support for sum-of-squares constraints with correlative sparsity

3) Support for moment-SOS relaxations for sparse polynomial optimization problems

4) Creation of symbolic polynomials with specified sign symmetries

5) Support for user-specified sign symmetries in sum-of-squares programs with arbitrary number of variables

## CDCS

CDCS (Cone Decomposition Conic Solver) is an open-source MATLAB solver for structured semidefinite programmes. It implements a selection of first-order algorithms, all based on the alternating direction method of multipliers (ADMM), for the solution of large semidefinite programmes (SDPs) characterised by a *chordal sparsity pattern*, and of SDPs characterised by *partial orthogonality*, which typically arise from sum-of-squares optimisation problems.

**Collaborators:** Yang Zheng (University of Oxford), Antonis Papachristodoulou (University of Oxford), Paul Goulart (University of Oxford), Andrew Wynn (Imperial College London).