GenRTR is the Generic Riemannian Trust-Region
package. GenRTR is a MATLAB package for the optimization of functions defined on
Riemannian manifolds. GenRTR currently provides two Riemannian trust-region methods:
the Riemannian Trust-Region (RTR) method (more info)
the Implicit Riemannian Trust-Region (IRTR) method (more info)
While the current emphasis concerns trust-region methods, the framework is
suitable for the implementation of any retraction-based optimization method. Future plans
involve the expansion of the framework to other optimization methods.
The optimization methods utilize MATLAB function handles to
access user-provided routines for the objective function, gradient, Hessian, retraction, etc. This enables the optimization solvers to be coded in a
generic manner and applied to minimization of arbitrary functions on arbitrary Riemannian manifolds. It also allows the encapsulation of a problem into a
single driver (e.g., rtreig), as opposed to a collection of files (e.g., f.m, grad.m).
GenRTR is released under a modified BSD open-source license, available here.
The package distribution currently contains drivers for the following applications:
Computation of the full symmetric eigenvalue decomposition over the orthogonal group (rtreig, rtreig2)
Computation of the dominant singular value decomposition over the Stiefel manifold (rtrdsvd, irtrdsvd)
Computation of extreme eigenspaces of a symmetric definite matrix pencil over the Grassmann manifold (rtresgev, irtresgev, tmesgev)