QP Parameters¶
regularize_threshold¶
Real value >= 1. Default value: -Inf
Ill-conditioning of the BFGS inverse Hessian approximations H may cause QP solver to have difficulty in solving either the steering or termination QPs. The BFGS inverse Hessian approximations H can be optionally regularized by limiting their condition numbers to regularize_threshold. Note that this regularization is only applied to the H matrices appearing in the QPs; the evolving BFGS inverse Hessian approximation itself is never regularized. NOTE: setting opts.regularize_threshold to inf disables any regularization (and thus disables even computing the condition number of H).
regularize_max_eigenvalues¶
Boolean value. Default value: False
If opts.regularize_threshold < inf, then NCVX’s default strategy to regularize the BFGS inverse Hessian approximation H is done by raising the smallest magnitude eigenvalues such that the condition number of the regularized version of H never exceeds opts.regularize_threshold. This default regularization should also help ensure that regularized version of H is numerically positive definite, since H may have tiny eigenvalues and in practice, these may have the wrong sign numerically (negative), particularly on nonsmooth problems. Alternatively, by setting this option to true, NCVX will instead apply regularization by lowering the largest eigenvalues of H but note that this mode does not attempt to maintain numerical positive definiteness. Also, if an eigenvalue of H is exactly zero, this mode will instead resort to raising the smallest eigenvalues of H on that particular iteration of NCVX.