https://github.com/albertosantini/quadprog
Module for solving quadratic programming problems with constraints
https://github.com/albertosantini/quadprog
quadratic-programming
Last synced: 6 months ago
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Module for solving quadratic programming problems with constraints
- Host: GitHub
- URL: https://github.com/albertosantini/quadprog
- Owner: albertosantini
- License: mit
- Created: 2011-09-13T15:44:12.000Z (almost 15 years ago)
- Default Branch: master
- Last Pushed: 2023-07-13T20:28:29.000Z (almost 3 years ago)
- Last Synced: 2025-01-09T11:33:30.309Z (over 1 year ago)
- Topics: quadratic-programming
- Language: JavaScript
- Homepage: https://github.com/albertosantini/node-conpa
- Size: 175 KB
- Stars: 33
- Watchers: 5
- Forks: 10
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
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README
QUADPROG
========
[](http://badge.fury.io/js/quadprog)
This module contains routines for solving quadratic programming problems,
written in JavaScript.
quadprog is a porting of a [R](http://www.r-project.org) package:
[quadprog](http://cran.r-project.org/web/packages/quadprog/), implemented in
Fortran.
It implements the dual method of Goldfarb and Idnani (1982, 1983) for solving
quadratic programming problems of the form
$$
\begin{aligned}
\text{minimize} \quad & -d^T b + \frac{1}{2} b^T D b \\
\text{subject to} \quad & A^T b \geq b_0
\end{aligned}
$$
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.
Installation and usage
======================
To install with [npm](http://github.com/isaacs/npm):
npm install quadprog
Usage:
import { solveQP } from "quadprog"; // ESM
or
const { solveQP } = require("quadprog"); // CJS
Tested locally with Node.js 22.x and with R 4.x.
Example
========
```r
## 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:
##
require(quadprog)
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)
# $solution
# [1] 0.4761905 1.0476190 2.0952381
# $value
# [1] -2.380952
# $unconstrained.solution
# [1] 0 5 0
# $iterations
# [1] 3 0
# $Lagrangian
# [1] 0.0000000 0.2380952 2.0952381
# $iact
# [1] 3 2
```
```javascript
import { solveQP } from "quadprog";
const Dmat = [], dvec = [], Amat = [], bvec = [];
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;
solveQP(Dmat, dvec, Amat, bvec)
// {
// solution: [
// <1 empty item>,
// 0.47619047619047616,
// 1.0476190476190477,
// 2.0952380952380953
// ],
// Lagrangian: [ <1 empty item>, 0, 0.23809523809523808, 2.0952380952380953 ],
// value: [ <1 empty item>, -2.380952380952381 ],
// unconstrained_solution: [ <1 empty item>, 0, 5, 0 ],
// iterations: [ <1 empty item>, 3, 0 ],
// iact: [ <1 empty item>, 3, 2, 0 ],
// message: ''
// }
```
Notes
=====
This is a strictly porting from Fortran code contained in R package [quadprog](https://cran.r-project.org/web/packages/quadprog/).
**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 `quadprog` via Numeric.js, don't forget the releases may
be not in sync.
Latest release is [here](https://github.com/albertosantini/quadprog).
Applications
============
- [ConPA](https://github.com/albertosantini/node-conpa)
- [Numeric.js](https://github.com/sloisel/numeric)
See also
========
- [GPU Accelerated JavaScript](https://github.com/gpujs/gpu.js)
- [Vincent Zoonekynd's Blog](http://zoonek.free.fr/blosxom/R/2012-06-01_Optimization.html)
- [fast.js](https://github.com/codemix/fast.js)
- [Vectorious](https://github.com/mateogianolio/vectorious)
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.