| qpspecial {pracma} | R Documentation |
Solves a special Quadratic Programming problem.
qpspecial(G, x, maxit = 100)
G |
|
x |
column vector of length |
maxit |
maximum number of iterates allowed; default 100. |
Solves the QP problem
min q(x) = || G*x ||_2^2 = x'*(G'*G)*x
s.t. sum(x) = 1
and x >= 0
The problem corresponds to finding the smallest vector (2-norm) in the
convex hull of the columns of G.
Returns a list with the following components:
x – optimal point attaining optimal value;
d = G*x – smallest vector in the convex hull;
q – optimal value found, = t(d) %*% d;
niter – number of iterations used;
info – error number:
= 0: everything went well, q is optimal,
= 1: maxit reached and final x is feasible,
= 2: something went wrong.
x may be missing, same as if requirements are not met; may stop with
an error if x is not feasible.
Matlab code by Anders Skajaa, 2010, under GPL license (HANSO toolbox); converted to R by Abhirup Mallik and Hans W. Borchers, with permission.
[Has to be found.]
G <- matrix(c(0.31, 0.99, 0.54, 0.20,
0.56, 0.97, 0.40, 0.38,
0.81, 0.06, 0.44, 0.80), 3, 4, byrow =TRUE)
qpspecial(G)
# $x
# [,1]
# [1,] 1.383697e-07
# [2,] 5.221698e-09
# [3,] 8.648168e-01
# [4,] 1.351831e-01
#
# $d
# [,1]
# [1,] 0.4940377
# [2,] 0.3972964
# [3,] 0.4886660
#
# $q
# [1] 0.6407121
#
# $niter
# [1] 6
#
# $info
# [1] 0