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Santini"},"repository":{"type":"git","url":"git+ssh://git@github.com/albertosantini/node-quadprog.git"},"readme":"QUADPROG\r\n========\r\n[![Build Status](https://travis-ci.org/albertosantini/node-quadprog.png)](https://travis-ci.org/albertosantini/node-quadprog)\r\n[![NPM version](https://badge.fury.io/js/quadprog.png)](http://badge.fury.io/js/quadprog)\r\n\r\nThis module contains routines for solving quadratic programming problems,\r\nwritten in JavaScript.\r\n\r\nquadprog is a porting of a [R](http://www.r-project.org) package:\r\n[quadprog](http://cran.r-project.org/web/packages/quadprog/), implemented in\r\nFortran.\r\n\r\nIt implements the dual method of Goldfarb and Idnani (1982, 1983) for solving\r\nquadratic programming problems of the form min(d T b + 1=2b T Db) with the\r\nconstraints AT b >= b0.\r\n\r\nReferences\r\n==========\r\n\r\nD. Goldfarb and A. Idnani (1982). Dual and Primal-Dual Methods for Solving\r\nStrictly Convex Quadratic Programs. In J. P. Hennart (ed.), Numerical Analysis,\r\nSpringer-Verlag, Berlin, pages 226–239.\r\n\r\nD. Goldfarb and A. Idnani (1983). A numerically stable dual method for solving\r\nstrictly convex quadratic programs. Mathematical Programming, 27, 1–33.\r\n\r\nExample\r\n========\r\n\r\n```\r\n// ##\r\n// ## Assume we want to minimize: -(0 5 0) %*% b + 1/2 b^T b\r\n// ## under the constraints: A^T b >= b0\r\n// ## with b0 = (-8,2,0)^T\r\n// ## and\r\n// ##     (-4 2  0)\r\n// ## A = (-3 1 -2)\r\n// ##     ( 0 0  1)\r\n// ## we can use solve.QP as follows:\r\n// ##\r\n// Dmat <- matrix(0,3,3)\r\n// diag(Dmat) <- 1\r\n// dvec <- c(0,5,0)\r\n// Amat <- matrix(c(-4,-3,0,2,1,0,0,-2,1),3,3)\r\n// bvec <- c(-8,2,0)\r\n// solve.QP(Dmat,dvec,Amat,bvec=bvec)\r\n\r\nvar qp = require('quadprog');\r\n\r\nvar Dmat = [], dvec = [], Amat = [], bvec = [], res;\r\n\r\nDmat[1] = [];\r\nDmat[2] = [];\r\nDmat[3] = [];\r\nDmat[1][1] = 1;\r\nDmat[2][1] = 0;\r\nDmat[3][1] = 0;\r\nDmat[1][2] = 0;\r\nDmat[2][2] = 1;\r\nDmat[3][2] = 0;\r\nDmat[1][3] = 0;\r\nDmat[2][3] = 0;\r\nDmat[3][3] = 1;\r\n\r\ndvec[1] = 0;\r\ndvec[2] = 5;\r\ndvec[3] = 0;\r\n\r\nAmat[1] = [];\r\nAmat[2] = [];\r\nAmat[3] = [];\r\nAmat[1][1] = -4;\r\nAmat[2][1] = -3;\r\nAmat[3][1] = 0;\r\nAmat[1][2] = 2;\r\nAmat[2][2] = 1;\r\nAmat[3][2] = 0;\r\nAmat[1][3] = 0;\r\nAmat[2][3] = -2;\r\nAmat[3][3] = 1;\r\n\r\nbvec[1] = -8;\r\nbvec[2] = 2;\r\nbvec[3] = 0;\r\n\r\nres = qp.solveQP(Dmat, dvec, Amat, bvec)\r\n```\r\n\r\nInstallation\r\n============\r\n\r\nTo install with [npm](http://github.com/isaacs/npm):\r\n\r\n    npm install quadprog\r\n\r\nTested locally with Node.js 10.x and with R 3.4.1.\r\n\r\nNotes\r\n=====\r\n\r\n**To maintain a one-to-one porting with the Fortran implementation, the array\r\nindex starts from 1 and not from zero. Please, be aware and give a look at the\r\nexamples in the test folder**.\r\n\r\nIf you are using `node-quadprog` via Numeric.js, don't forget the releases may\r\nbe not in sync. Latest release is here.\r\n\r\nApplications\r\n============\r\n\r\n- [ConPA](https://github.com/albertosantini/node-conpa)\r\n- [Numeric.js](https://github.com/sloisel/numeric)\r\n\r\nSee also\r\n========\r\n\r\n- [GPU Accelerated JavaScript](https://github.com/gpujs/gpu.js)\r\n- [Vincent Zoonekynd's Blog](http://zoonek.free.fr/blosxom/R/2012-06-01_Optimization.html)\r\n- [fast.js](https://github.com/codemix/fast.js)\r\n- [Vectorious](https://github.com/mateogianolio/vectorious)\r\n- [More on Quadratic Programming in R](http://quantitate.blogspot.it/2015/02/more-on-quadratic-progamming-in-r.html)\r\n\r\nMethods\r\n=======\r\n\r\nsolveQP(Dmat, dvec, Amat, bvec, meq=0, factorized=FALSE)\r\n-------\r\n\r\n**Arguments**\r\n\r\n- *Dmat* matrix appearing in the quadratic function to be minimized.\r\n\r\n- *dvec* vector appearing in the quadratic function to be minimized.\r\n\r\n- *Amat* matrix deﬁning the constraints under which we want to minimize the\r\nquadratic function.\r\n\r\n- *bvec* vector holding the values of b0 (defaults to zero).\r\n\r\n- *meq* the ﬁrst meq constraints are treated as equality constraints, all\r\nfurther as inequality constraints (defaults to 0).\r\n\r\n- *factorized* logical ﬂag: if TRUE, then we are passing R1 (where D = RT R)\r\ninstead of the matrix D in the argument Dmat.\r\n\r\n**Value**\r\n\r\nAn object with the following property:\r\n\r\n- *solution* vector containing the solution of the quadratic programming\r\nproblem.\r\n\r\n- *value* scalar, the value of the quadratic function at the solution\r\n\r\n- *unconstrained.solution* vector containing the unconstrained minimizer of the\r\nquadratic function.\r\n\r\n- *iterations* vector of length 2, the ﬁrst component contains the number of\r\niterations the algorithm needed, the second indicates how often constraints\r\nbecame inactive after becoming active ﬁrst.\r\n\r\n- *Lagrangian* vector with the Lagrangian multipliers at the solution.\r\n\r\n- *iact* vector with the indices of the active constraints at the solution.\r\n\r\n- *message* string containing an error message, if the call failed, otherwise empty.\r\n\r\nTesting\r\n=======\r\n\r\nBase test cases are in json formatted files with the name `<name>-data.json`.\r\nThese can be passed into `solve.R` to create the standard R results for solveQP with the name `<name>-result.json`.\r\nThe standard usage is `Rscript solve.R *-data.json`, but you may wish to only create result files for specific tests.\r\nThe combination of these files is then used by `solution-test.js` and `bench.js`.\r\n\r\n\r\nAdding Tests\r\n------------\r\n\r\nTo 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.\r\n","homepage":"https://github.com/albertosantini/node-quadprog#readme","keywords":["quadprog","solving","quadratic"],"bugs":{"url":"https://github.com/albertosantini/node-quadprog/issues"},"license":"MIT","readmeFilename":"README.md"}