Special Quadratic Programming Solver
Solves a special Quadratic Programming problem.
qpspecial(G, x, maxit = 100) qpsolve(d, A, b, meq = 0, tol = 1e-07)
G |
|
x |
column vector of length |
maxit |
maximum number of iterates allowed; default 100. |
d |
Linear term of the quadratic form. |
A, b |
Linear equality and inequality constraints. |
meq |
First meq rows are used as equality constraints. |
tol |
Tolerance used for stopping the iteration. |
qpspecial solves the special QP problem:
min q(x) = || G*x ||_2^2 = x'*(G'*G)*xs.t. sum(x) = 1and x >= 0
The problem corresponds to finding the smallest vector (2-norm) in the
convex hull of the columns of G.
qpsolve solves the more general QP problem:
min q(x) = 0.5 t(x)*x - d xs.t. A x >= b
with A x = b for the first meq rows.
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
# Example from quadprog::solve.QP
d <- c(0,5,0)
A <- matrix(c(-4,-3,0,2,1,0,0,-2,1),3,3)
b <- c(-8,2,0)
qpsolve(d, A, b)
## $sol
## [1] 0.4761905 1.0476190 2.0952381
## $val
## [1] -2.380952
## $niter
## [1] 3Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.