solve.QP {quadprog}R Documentation

Solve a Quadratic Programming Problem


This routine implements the dual method of Goldfarb and Idnani (1982, 1983) for solving quadratic programming problems of the form min(-d^T b + 1/2 b^T D b) with the constraints A^T b >= b_0.


solve.QP(Dmat, dvec, Amat, bvec, meq=0, factorized=FALSE)


Dmat matrix appearing in the quadratic function to be minimized.
dvec vector appearing in the quadratic function to be minimized.
Amat matrix defining the constraints under which we want to minimize the quadratic function.
bvec vector holding the values of b_0 (defaults to zero).
meq the first meq constraints are treated as equality constraints, all further as inequality constraints (defaults to 0).
factorized logical flag: if TRUE, then we are passing R^(-1) (where D = R^T R) instead of the matrix D in the argument Dmat.


a list with the following components:

solution vector containing the solution of the quadratic programming problem.
value scalar, the value of the quadratic function at the solution
unconstrained.solution vector containing the unconstrained minimizer of the quadratic function.
iterations vector of length 2, the first component contains the number of iterations the algorithm needed, the second indicates how often constraints became inactive after becoming active first. vector with the indices of the active constraints at the solution.


Goldfarb, D. and Idnani, A. (1982). Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs. In Numerical Analysis J.P. Hennart, ed. Springer-Verlag, Berlin. pp. 226-239.

Goldfarb, D. and Idnani, A. (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming 27, 1-33.

See Also



# 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 solve.QP as follows:
Dmat       <- matrix(0,3,3)
diag(Dmat) <- 1
dvec       <- c(0,5,0)
Amat       <- matrix(c(-4,-3,0,2,1,0,0,-2,1),3,3)
bvec       <- c(-8,2,0)

[Package quadprog version 1.4-11 Index]