pystop.solver.slpg_smooth

X, output_dict = slpg_smooth( obj_fun, manifold, Xinit = None, maxit= 100, gtol = 1e-5, post_process = True, verbosity = 2, **kwargs)

Minimize a smooth objective function fun over the Stiefel manifold starting from Xinit by the penalty-free infeasible first-order method (SLPG). The word ''penalty-free'' means SLPG does not need the penalty parameter β. For more details, we suggest the interested reader refer to a related paper.

 

Input arguments

 

Output results

 

Example

In these examples, we solve the following nonlinear eigenvalue problem

minXSn,p 12tr(XLX)+α4ρLρ,

where ρ=Diag(XX), and L denotes the pseudo-inverse of the positive definite matrix L.

The following examples introduces how to apply PenCF to solve this problem.