Add to ORKGWe use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive semidefinite rank, and their symmetric analogues: the completely positive rank and the completely positive semidefinite rank. We study the convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples
Thesis (Ph.D.)--University of Washington, 2014The positive semidefinite (psd) rank of a nonnegative ...
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the...
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatori...
We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetr...
This paper investigates the problem of approximating the global minimum of a positive semidefinite H...
Abstract — After a brief overview of the problem of finding the extremal (minimum or maximum) rank p...
International audienceWe consider the problem of minimizing a linear function over an affine section...
International audienceWe consider the problem of minimizing a linear function over an affine section...
The nonnegative rank of an entrywise nonnegative matrix A ∈ R[m×n over +] is the smallest integer r ...
Nonnegative matrix factorization (NMF) consists in finding two nonnegative matrices whose product is...
Thesis (Ph.D.)--University of Washington, 2014The positive semidefinite (psd) rank of a nonnegative ...
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the...
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of ...
Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatori...
We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetr...
This paper investigates the problem of approximating the global minimum of a positive semidefinite H...
Abstract — After a brief overview of the problem of finding the extremal (minimum or maximum) rank p...
International audienceWe consider the problem of minimizing a linear function over an affine section...
International audienceWe consider the problem of minimizing a linear function over an affine section...
The nonnegative rank of an entrywise nonnegative matrix A ∈ R[m×n over +] is the smallest integer r ...
Nonnegative matrix factorization (NMF) consists in finding two nonnegative matrices whose product is...
Thesis (Ph.D.)--University of Washington, 2014The positive semidefinite (psd) rank of a nonnegative ...
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the...
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the...