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
See also
- GPU Accelerated JavaScript
- Vincent Zoonekynd's Blog
- fast.js
- Vectorious
- More on Quadratic Programming in R
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.