The Manopt toolbox: making optimization on manifolds easy

Optimization on manifolds is a powerful paradigm to address nonlinear optimization problems. It has been successful in solving matrix problems with low-rank or orthogonality constraints for example. The theory for smooth optimization on manifolds is well-understood, with most standard algorithms (steepest descent, conjugate gradients, trust-regions...) available with convergence guarantees matching the standard theory. We propose a new Matlab toolbox called Manopt. Its purpose is to make optimization on manifolds feel as simple as standard nonlinear optimization. We will motivate the importance of this class of optimization problems in applications and illustrate how the toolbox can be used to address them. http://www.manopt.org