QUADPROG

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.

References

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.

Example

// ##
// ## 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)

Installation

To install with npm:

npm install quadprog

Tested locally with Node.js 10.x and with R 3.4.1.

Notes

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.

Applications

Methods

solveQP(Dmat, dvec, Amat, bvec, meq=0, factorized=FALSE)

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.

Testing

Base test cases are in json formatted files with the name <name>-data.json. These can be passed into solve.R to create the standard R results for solveQP with the name <name>-result.json. The standard usage is Rscript solve.R *-data.json, but you may wish to only create result files for specific tests. The combination of these files is then used by solution-test.js and bench.js.

Adding Tests

To add a new test simply create a file called <name>-data.json in the test directory, and then call Rscript solve.R <name>-data.json and commit the results.

albertosantini / quadprog