quadprog

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
============

- ConPA
- Numeric.js

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 -data.json.
These can be passed into solve.R to create the standard R results for solveQP with the 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 -data.json in the test directory, and then call Rscript solve.R -data.json` and commit the results.