polynomial-optimization

Solver for Large-Scale Rank-One Semidefinite Relaxations

Irene is a python package that aims to be a toolkit for global optimization problems that can be realized algebraically. It generalizes Lasserre's Relaxation method to handle theoretically any optimization problem with bounded feasibility set. The method is based on solutions of generalized truncated moment problems over commutative real algebras.

Master's thesis "Semidefinite Programming for Geometric Problems in Computer Vision".

Code for the paper "The speed of traveling waves in a FKPP-Burgers system"

Code for senior thesis titled "Novel results on Computational Methods for Polynomial Optimization", advised by Amir Ali Ahmadi at Princeton University in the 2017-2018 academic year.

Code for the paper "Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization"

Certified computational study of the gap shape of degree-4 sum-of-squares relaxations of unique games. A null result on the main question, two proved theorems on Paley graphs, and a structural determination of the degree-4 extension. Fully reproducible: 132 checks, 0 mismatches.

Computational study of Putinar and Schmüdgen Sum-of-Squares relaxations for one-dimensional polynomial obstacle avoidance, including exactness, geometry, and solver-scaling experiments.

Research toolbox for polynomial optimization using Sum-of-Squares (SOS) and moment relaxations (SDP, SOCP, chordal methods)

SOS methods vs. metaheuristics for multi-objective polynomial optimization — code, data, and reproducibility artifacts

Solve SOSTOOLS sum-of-squares programs, including matrix SOS constraints, without semidefinite programming: interpolant SOS cones and a non-symmetric interior-point method in MATLAB and Octave, with certified solutions. Builds on Papp-Yıldız and Kapelevich-Coey-Vielma (Hypatia).