5 papers · 1 filter
Sharpness and well-conditioning of nonsmooth convex formulations in statistical signal recovery
Lijun Ding, Alex L. Wang
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract p…
New notions of simultaneous diagonalizability of quadratic forms with applications to QCQPs
Alex L. Wang, Rujun Jiang
A set of quadratic forms is simultaneously diagonalizable via congruence (SDC) if there exists a basis under which each of the quadratic forms is diagonal. This property appears na…
Hidden convexity, optimization, and algorithms on rotation matrices
Akshay Ramachandran, Kevin Shu, Alex L. Wang
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices . Such problems are nonconvex due t…
On semidefinite descriptions for convex hulls of quadratic programs
Alex L. Wang, Fatma Kilinc-Karzan
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural conv…
Accelerated first-order methods for a class of semidefinite programs
Alex L. Wang, Fatma Kilinc-Karzan
This paper introduces a new storage-optimal first-order method (FOM), CertSDP, for solving a special class of semidefinite programs (SDPs) to high accuracy. The class of SDPs that…