QP Parameters
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regularize_threshold
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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.