The discovery of scientific formulae that parsimoniously explain natural phenomena and
align with existing background theory is a key goal in science. Historically, scientists have …

Numerous interesting properties in nonlinear systems analysis can be written as polynomial
optimization problems with nonconvex sum-of-squares problems. To solve those problems …

A polynomial matrix inequality is a statement that a symmetric polynomial matrix is positive
semidefinite over a given constraint set. Polynomial matrix optimization concerns minimizing …

We study spurious second-order stationary points and local minima in a nonconvex low-rank
formulation of sum-of-squares optimization on a real variety $ X $. We reformulate the …

The discovery of scientific formulae that parsimoniously explain natural phenomena and
align with existing background theory is a key goal in science. Historically, scientists have …

Sum of squares (SOS) optimization is a powerful technique for solving problems where the
positivity of a polynomials must be enforced. The common approach to solve an SOS …

We introduce a family of symmetric convex bodies called generalized ellipsoids of degree $
d $(GE-$ d $ s), with ellipsoids corresponding to the case of $ d= 0$. Generalized ellipsoids …

We consider the least squares projection onto the behavior for linear time-invariant (LTI)
single-input single-output (SISO) models, in which the observed input-output data are …

En este trabajo se estudia el paper" Low-rank univariate sum of squares has no spurious
local minima" de Pablo Parrillo, et al. En el que se trata el problema de estableces si un …

This monograph is devoted to applications of the Kronecker decomposition approach for the
stability and stabilization of linear systems with nontrivial distributed delays through the …