Type: Package
Title: Interface to the 'qpmad' Quadratic Programming Solver
Version: 1.1.0-0
Date: 2021-06-23
Description: Efficiently solve quadratic problems with linear inequality, equality and box constraints. The method used is outlined in D. Goldfarb, and A. Idnani (1983) <doi:10.1007/BF02591962>.
License: GPL (≥ 3)
URL: https://github.com/anderic1/qpmadr
BugReports: https://github.com/anderic1/qpmadr/issues
Depends: R (≥ 3.0.2)
Imports: Rcpp, checkmate
LinkingTo: Rcpp, RcppEigen (≥ 0.3.3.3.0)
RoxygenNote: 7.1.1
Encoding: UTF-8
Suggests: tinytest
NeedsCompilation: yes
Packaged: 2021-06-23 08:36:27 UTC; hhh
Author: Eric Anderson [aut, cre], Alexander Sherikov [cph, ctb]
Maintainer: Eric Anderson <anderic1@gmx.com>
Repository: CRAN
Date/Publication: 2021-06-23 10:00:02 UTC

Set qpmad parameters

Description

Conveniently set qpmad parameters. Please always use named arguments since parameters can change without notice between releases. In a future version specifying the argument names will be mandatory.

Usage

qpmadParameters(
  isFactorized = FALSE,
  maxIter = -1,
  tol = 1e-12,
  checkPD = TRUE,
  factorizationType = "NONE",
  withLagrMult = FALSE,
  returnInvCholFac = FALSE
)

Arguments

isFactorized

Deprecated, will be removed in a future version. Please use factorizationType instead. If TRUE then H is a lower Cholesky factor, overridden byfactorizationType.

maxIter

Maximum number of iterations, if not positive then no limit.

tol

Convergence tolerance.

checkPD

Deprecated. Ignored, will be removed in a future release.

factorizationType

IF "NONE" then H is a Hessian (default), if "CHOLESKY" then H is a (lower) cholesky factor. If "INV_CHOLESKY" then H is the inverse of a cholesky factor, i.e. such that the Hessian is given by inv(HH').

withLagrMult

If TRUE then the Lagrange multipliers of the inequality constraints, along with their indexes and an upper / lower side indicator, will be returned.

returnInvCholFac

If TRUE then also return the inverse Cholesky factor of the Hessian.

Value

a list suitable to be used as the pars-argument to solveqp

See Also

solveqp

Examples


qpmadParameters(withLagrMult = TRUE)

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:

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)