Biconvex Relaxation for Semidefinite Programming in Computer Vision [article]

Sohil Shah, Abhay Kumar, Carlos Castillo, David Jacobs, Christoph Studer, Tom Goldstein
2016 arXiv   pre-print
Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately solve large-scale semidefinite problems (SDPs) at low complexity. Our approach, referred to as biconvex relaxation (BCR), transforms a general SDP into a specific biconvex optimization problem, which can then be solved in the original, low-dimensional variable
more » ... pace at low complexity. The resulting biconvex problem is solved using an efficient alternating minimization (AM) procedure. Since AM has the potential to get stuck in local minima, we propose a general initialization scheme that enables BCR to start close to a global optimum - this is key for our algorithm to quickly converge to optimal or near-optimal solutions. We showcase the efficacy of our approach on three applications in computer vision, namely segmentation, co-segmentation, and manifold metric learning. BCR achieves solution quality comparable to state-of-the-art SDP methods with speedups between 4X and 35X. At the same time, BCR handles a more general set of SDPs than previous approaches, which are more specialized.
arXiv:1605.09527v2 fatcat:6ndyravgwndwpcpeyvckxnoygi