solveqp {qpmadr}

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. qpmadParameters.

h

Optional, vector of length n.

lb, ub

Optional, lower/upper bounds of x. Will be repeated n times if length is one.

A

Optional, constraints matrix of dimension p*n, where each row corresponds to a constraint. For equality constraints let corresponding elements in Alb equal those in Aub

Alb, Aub

Optional, lower/upper bounds for Ax.

pars

Optional, qpmad-solver parameters, conveniently set with qpmadParameters

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 definite

• 1: Inconsistent

• 2: Infeasible equality

• 3: Infeasible inequality

• 4: Maximal number of iterations

See Also

qpmadParameters

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)