8 papers · 1 filter
Nonsmooth rank-one matrix factorization landscape
Cédric Josz, Lexiao Lai
We provide the first positive result on the nonsmooth optimization landscape of robust principal component analysis, to the best of our knowledge. It is the object of several conje…
Verifying Global Optimality of Candidate Solutions to Polynomial Optimization Problems using a Determinant Relaxation Hierarchy
Sikun Xu, Ruoyi Ma, Daniel K. Molzahn +2
We propose a method for verifying that a given feasible point for a polynomial optimization problem is globally optimal. The approach relies on the Lasserre hierarchy and the resul…
The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms
Sogol Babaeinejadsarookolaee, Adam Birchfield, Richard D. Christie +20
In recent years, the power systems research community has seen an explosion of novel methods for formulating the AC power flow equations. Consequently, benchmarking studies using t…
On the Absence of Spurious Local Trajectories in Time-varying Nonconvex Optimization
S. Fattahi, C. Josz, Y. Ding +3
In this paper, we study the landscape of an online nonconvex optimization problem, for which the input data vary over time and the solution is a trajectory rather than a single poi…
Transient Stability Analysis of Power Systems via Occupation Measures
Cedric Josz, Daniel K. Molzahn, Matteo Tacchi +1
We propose the application of occupation measure theory to the classical problem of transient stability analysis for power systems. This enables the computation of certified inner…
Algorithm for Optimization and Interpolation based on Hyponormality
Cédric Josz
On one hand, consider the problem of finding global solutions to a polynomial optimization problem and, on the other hand, consider the problem of interpolating a set of points wit…