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 …

We study the semialgebraic structure of D_r, the set of nonnegative tensors of nonnegative
rank not more than r, and use the results to infer various properties of nonnegative tensor …

We use techniques from (tracial noncommutative) polynomial optimization to formulate
hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In …

We provide a complete classification of the extreme rays of the 6 * 6 6× 6 copositive cone
COP^ 6 COP 6. We proceed via a coarse intermediate classification of the possible minimal …

We study nonconvex quadratic minimization problems under (possibly nonconvex)
quadratic and linear constraints, characterizing both Lagrangian and semi-Lagrangian dual …

In this paper we construct new families of extremal copositive matrices in arbitrary dimension
by an algorithmic procedure. Extremal copositive matrices are organized in relatively open …

In a Standard Quadratic Optimization Problem (StQP), a possibly indefinite quadratic form
(the simplest nonlinear function) is extremized over the standard simplex, the simplest …

An n * nn× n matrix X is called completely positive semidefinite (cpsd) if there exist d * dd× d
Hermitian positive semidefinite matrices {P_i\} _ i= 1^ n P ii= 1 n (for some d ≥ 1 d≥ 1) such …

A real symmetric matrix M is completely positive semidefinite if it admits a Gram
representation by (Hermitian) positive semidefinite matrices of any size d. The smallest such …

We establish a geometric condition guaranteeing exact copositive relaxation for the
nonconvex quadratic optimization problem under two quadratic and several linear …