box_qp_f
solves the minimization problem
\mathrm{minimize}_{u}\;\; (b +u)' Q (b + u );\;\; \mathrm{subject\;\; to}\;\; \u\_∞ ≤q ρ
where Q_{m \times m} is symmetric PSD, u,b \in \Re^m. The algorithm used is oneatatime cyclical coordinate descent.
1  box_qp_f(Q, u, b, rho, Maxiter, tol = 10^4)

Q 
(Required) is a symmetric PSD matrix of dimension m \times m. This is a problem parameter. 
u 
(Required) is the optimization variable, a vector of length m.
The value of If a suitable starting point is unavailable, start with 
b 
(Required) is a vector of length m, this is a problem parameter. 
rho 
(Required) is the degree of shrinkage. This is a nonnegative scalar. 
Maxiter 
(Required) is an integer denoting the maximum number of iterations (full sweeps across all the m variables), to be performed by

tol 
is the convergence tolerance. It is a real positive number (defaults to 10^4).

This box QP function is a R wrapper to a Fortran code. This is primarily meant
to be called from the R function dpglasso
.
One needs to be very careful (as in supplying the inputs of the progra properly) while using this as a stand alone program.
u 
the optimal value of the argument 
grad_vec 
the gradient of the objective function at 
Rahul Mazumder and Trevor Hastie
This algorithm is used as a part of the algorithm DPGLASSO described in our paper: “The Graphical Lasso: New Insights and Alternatives by Rahul Mazumder and Trevor Hastie" available at http://arxiv.org/abs/1111.5479
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