This module contains routines for solving quadratic programming problems, written in JavaScript.
quadprog is a porting of a R package: quadprog, implemented in Fortran.
It implements the dual method of Goldfarb and Idnani (1982, 1983) for solving quadratic programming problems of the form min(d T b + 1=2b T Db) with the constraints AT b >= b0.
D. Goldfarb and A. Idnani (1982). Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs. In J. P. Hennart (ed.), Numerical Analysis, Springer-Verlag, Berlin, pages 226–239.
D. Goldfarb and A. Idnani (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming, 27, 1–33.
// ##
// ## 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)
// solve.QP(Dmat,dvec,Amat,bvec=bvec)
var qp = require('quadprog');
var Dmat = [], dvec = [], Amat = [], bvec = [], res;
Dmat[1] = [];
Dmat[2] = [];
Dmat[3] = [];
Dmat[1][1] = 1;
Dmat[2][1] = 0;
Dmat[3][1] = 0;
Dmat[1][2] = 0;
Dmat[2][2] = 1;
Dmat[3][2] = 0;
Dmat[1][3] = 0;
Dmat[2][3] = 0;
Dmat[3][3] = 1;
dvec[1] = 0;
dvec[2] = 5;
dvec[3] = 0;
Amat[1] = [];
Amat[2] = [];
Amat[3] = [];
Amat[1][1] = -4;
Amat[2][1] = -3;
Amat[3][1] = 0;
Amat[1][2] = 2;
Amat[2][2] = 1;
Amat[3][2] = 0;
Amat[1][3] = 0;
Amat[2][3] = -2;
Amat[3][3] = 1;
bvec[1] = -8;
bvec[2] = 2;
bvec[3] = 0;
res = qp.solveQP(Dmat, dvec, Amat, bvec)
To install with npm:
npm install quadprog
Tested locally with Node.js 5.x and with R 3.2.2.
To maintain a one-to-one porting with the Fortran implementation, the array index starts from 1 and not from zero. Please, be aware and give a look at the examples in the test folder.
If you are using node-quadprog
via Numeric.js, don't forget the releases may
be not in sync. Latest release is here.
Arguments
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 b0 (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 R1 (where D = RT R) instead of the matrix D in the argument Dmat.
Value
An object with the following property:
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.
Lagrangian vector with the Lagrangian multipliers at the solution.
iact vector with the indices of the active constraints at the solution.
message string containing an error message, if the call failed, otherwise empty.