Software and Codes
Software
ManiSDP aims to solve the low-rank linear semidefinite program (SDP) via manifold optimization. Here, low-rank means the SDP admits a low-rank optimal solution.
MiniSOC computes (approximately) optimal second-order cone representations for a weighted geometric mean inequality.
TSSOS is a Julia package for sparse polynomial optimization.
SONCSOCP is a Julia package for uncontrained sparse polynomial optimization based on the second-order cone representation of SONC cones.
SparseJSR is a Julia package for computing joint spectral radii based on sparse SOS decompositions.
ChordalGraph is an extension of the Julia package Graphs to handle chordal graphs.
NCTSSOS is a Julia package for sparse noncommutative polynomial optimization.
Codes and experimental material
ramdonly generated nc polynomials
random matrices for Table II
random control systems for Table III
random control systems for Table IV
g20
g40
g60
g80
g100
g120
g140
g160
g180
g200
poly_type1: randomly generated polynomials of type I for unconstrained polynomial optimization
poly_type2: randomly generated polynomials of type II for unconstrained polynomial optimization
cpoly_type2: randomly generated polynomials of type II for constrained polynomial optimization
Bistability is the code for the numerical experiments in the paper Bistability of Sequestration Networks.