A ubiquitous problem in quantum physics is to understand the ground-state properties of
many-body systems. Confronted with the fact that exact diagonalization quickly becomes …

This paper introduces state polynomials, ie, polynomials in noncommuting variables and
formal states of their products. A state analog of Artin's solution to Hilbert's 17th problem is …

We explore a new type of sparsity for the generalized moment problem (GMP) that we call
ideal-sparsity. In this setting, one optimizes over a measure restricted to be supported on the …

In this paper, we consider the tensor absolute value equations (TAVEs). When one tensor is
row diagonal with odd order, we show that the TAVEs can be reduced to an algebraic …

This paper explores methods for verifying the properties of Binary Neural Networks (BNNs),
focusing on robustness against adversarial attacks. Despite their lower computational and …

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 …

This work derives upper bounds on the convergence rate of the moment-sum-of-squares
hierarchy with correlative sparsity for global minimization of polynomials on compact basic …

The Moment-SOS hierarchy, first introduced in optimization in 2000, is based on the theory
of the S-moment problem and its dual counterpart: polynomials that are positive on S. It turns …

In this paper, we consider polynomial optimization with correlative sparsity. We construct
correlatively sparse Lagrange multiplier expressions (CS-LMEs) and propose CS-LME …

We introduce a convergent hierarchy of lower bounds on the minimum value of a real form
over the unit sphere. The main practical advantage of our hierarchy over the real sum-of …