160 citations · 693 across the 40 of their papers we have counts for
18 papers · 1 filter
Lifting for Simplicity: Concise Descriptions of Convex Sets
Hamza Fawzi, João Gouveia, Pablo A. Parrilo +2
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the or…
Spectrahedral Lifts of Convex Sets
Rekha R. Thomas
Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be express…
On the local stability of semidefinite relaxations
Diego Cifuentes, Sameer Agarwal, Pablo A. Parrilo +1
We consider a parametric family of quadratically constrained quadratic programs (QCQP) and their associated semidefinite programming (SDP) relaxations. Given a nominal value of the…
The Euclidean Distance Degree of Orthogonally Invariant Matrix Varieties
Dmitriy Drusvyatskiy, Hon-Leung Lee, Giorgio Ottaviani +1
We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustra…
Counting real critical points of the distance to orthogonally invariant matrix sets
Dmitriy Drusvyatskiy, Hon-Leung Lee, Rekha R. Thomas
Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of criti…
Positive semidefinite rank
Hamza Fawzi, João Gouveia, Pablo A. Parrilo +2
Let M be a p-by-q matrix with nonnegative entries. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices $A_…