solveqp {qpmadr} | R Documentation |
Quadratic Programming
Description
Solves
argmin 0.5 x' H x + h' x
s.t.
lb_i \leq x_i \leq ub_i
Alb_i \leq (A x)_i \leq Aub_i
Usage
solveqp(
H,
h = NULL,
lb = NULL,
ub = NULL,
A = NULL,
Alb = NULL,
Aub = NULL,
pars = list()
)
Arguments
H |
Symmetric positive definite matrix, n*n. Can also be a (inverse) Cholesky factor cf.
|
h |
Optional, vector of length n. |
lb , ub |
Optional, lower/upper bounds of |
A |
Optional, constraints matrix of dimension p*n, where each row corresponds to a constraint. For equality constraints let corresponding elements in |
Alb , Aub |
Optional, lower/upper bounds for |
pars |
Optional, qpmad-solver parameters, conveniently set with |
Value
At least one of lb
, ub
or A
must be specified. If A
has been
specified then also at least one of Alb
or Aub
. Returns a list with elements solution
(the solution vector),
status
(a status code) and message
(a human readable message). If status
= 0
the algorithm has converged.
Possible status codes:
0
: Ok-1
: Numerical issue, matrix (probably) not positive definite1
: Inconsistent2
: Infeasible equality3
: Infeasible inequality4
: Maximal number of iterations
See Also
Examples
## Assume we want to minimize: -(0 5 0) %*% b + 1/2 b^T b
## under the constraints: A^T b >= b0
## with b0 = (-8,2,0)^T
## and (-4 2 0)
## A = (-3 1 -2)
## ( 0 0 1)
## we can use solveqp as follows:
##
Dmat <- diag(3)
dvec <- c(0,-5,0)
Amat <- t(matrix(c(-4,-3,0,2,1,0,0,-2,1),3,3))
bvec <- c(-8,2,0)
solveqp(Dmat,dvec,A=Amat,Alb=bvec)