pracma (version 1.9.3)

qpspecial: Special Quadratic Programming Solver

Description

Solves a special Quadratic Programming problem.

Usage

qpspecial(G, x, maxit = 100)

Arguments

G

m x n-matrix.

x

column vector of length n, the initial (feasible) iterate; if not present (or requirements on x0 not met), x0 will be found.

maxit

maximum number of iterates allowed; default 100.

Value

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.

Details

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.

References

[Has to be found.]

Examples

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