This CRAN task view contains a list of packages which offer facilities for solving optimization problems. Although every regression model in statistcs solves an optimization problem they are not part of this view. If you are looking for regression methods, the following views will contain useful starting points: Multivariate, SocialSciences, Robust among others. The focus of this task view is on General Purpose Continuous Solvers , Mathematical Programming Solvers and Specific Applications in Optimization . Packages are categorized in these three sections.

Many packages provide functionality for more than one of the subjects listed at the end of this task view. E.g., mixed integer linear programming solvers typically offer standard linear programming routines like the simplex algorithm. Therefore following each package description a list of abbreviations describes the typical features of the optimizer (i.e., the problems which can be solved). The full names of the abbreviations given in square brackets can be found at the end of this task view under Classification According to Subject .

If you think that some package is missing from the list, please let me know.

General Purpose Continuous Solvers

• Package stats offers several general purpose optimization routines. First, function optim() provides an implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, bounded BFGS, conjugate gradient, Nelder-Mead, and simulated annealing (SANN) optimization methods. It utilizes gradients, if provided, for faster convergence. Typically it is used for unconstrained optimization but includes an option for box-constrained optimization. Additionally, for minimizing a function subject to linear inequality constraints stats contains the routine constrOptim(). For one-dimensional unconstrained function optimization there is optimize() which searches an interval for a minimum or maximum. Then there is nlm which is used for solving nonlinear unconstrained minimization problems. Eventually, nlminb() offers unconstrained and constrained optimization using PORT routines. [RGA, QN]
• clue contains the function sumt() for solving constrained optimization problems via the sequential unconstrained minimization technique (SUMT).
• Package gsl provides BFGS, conjugate gradient, steepest descent, and Nelder-Mead algorithms. It uses a "line search" approach via the function multimin(). It is based on the GNU Scientific Library (GSL). [RGA, QN]
• Package maxLik provides a general purpose Newton-Raphson optimizer maxNR() as well as wrapper to methods, implemented in optim(). It supports fitting a submodel by specifying constant parameters.
• subplex provides unconstrained function optimization based on a subspace searching simplex method.
• Package ucminf implements an algorithm of quasi-Newtonian type for nonlinear unconstrained optimization. [QN]
• In package trust, a routine with the same name offers local optimization based on the "trust region" approach.
• Package nleqslv provides a function nleqslv() implementing Newton and Broyden methods with line search and trust region global strategies for solving medium sized system of nonlinear equations.
• In package gafit gafit() uses a genetic algorithm approach to find the minimum of a one-dimensional function.
• Package genalg contains rbga(), an implementation of a genetic algorithm for multi-dimensional function optimization.
• Package rgenoud offers genoud(), a routine which is capable of solving complex function minimization/maximization problems by combining evolutionary algorithms with a derivative-based (quasi-Newtonian) approach.
• Package DEoptim provides a global optimizer based on the differential evolution algorithm.

Mathematical Programming Solvers

This section provides an overview of open source as well as commercial optimizers. Which type of mathematical programming problem can be solved by a certain package or function can be seen from the abbreviations in square brackets. For a classification by subject see the list at the end of this task view.

• Package linprog solves linear programming problems using the function solveLP() (the solver is based on lpSolve) and can read model files in MPS format. [LP]
• In package quadprog solve.QP() solves quadratic programming problems with linear equality and inequality constraints. [QP]
• BB contains the function spg() providing a spectral projected gradient method for large scale optimization with simple constraints. It takes a nonlinear objective function as an argument as well as basic constraints. Furthermore, BB contains two functions ( dfsane() and sane()) for using the spectral gradient method for solving a nonlinear system of equations.
• In the boot package there is a routine called simplex() which realizes the two-phase tableau simplex method for (relatively small) linear programming problems. [LP]
• kernlab contains the function ipop for solving quadratic programming problems using interior point methods. [IPM, QP]
• limSolve offers to solve linear or quadratic optimization functions. [LP, QP]
• LowRankQP primal/dual interior point method solving quadratic programming problems [IPM, QP]
• Package rcdd offers the function lpcdd() for solving linear programs with exact arithmetic using the GNU Multiple Precision (GMP) library. [LP]
• In package Rdonlp2 function donlp2(), a wrapper for the DONLP2 solver, offers the minimization of smooth nonlinear functions and constraints. DONLP2 can be used freely for any kind of research purposes, otherwise it requires licensing. [GO, NLP]
• Rsolnp is currently being developed on R-Forge in project rino. This package offers general nonlinear optimization using the augmented lagrange multiplier method. [NLP]

Interfaces to Open Source Optimizers

• Package lpSolve contains the routine lp() to solve LPs and MILPs by calling the freely available solver lp_solve . This solver is based on the revised simplex method and a branch-and-bound (B&B) approach. It supports semi-continuous variables and Special Ordered Sets (SOS). Furthermore lp.assign() and lp.transport() are aimed at solving assignment problems and transportation problems, respectively. Additionally, there is the package lpSolveAPI which provides an R interface to the low level API routines of lp_solve (see also project lpsolve on R-Forge ). lpSolveAPI supports reading linear programs from files in lp and MPS format. [BP, IP, LP, MILP, SPLP]
• Package glpk as well as package Rglpk provide an interface to the GNU Linear Programming Kit (GLPK). Whereas the former provides high level access to low level routines the latter offers a high level routine Rglpk_solve_LP() to solve MILPs using GLPK. Both packages offer the possibility to use models formulated in the MPS format. [BP, IP, IPM, LP, MILP]
• Rsymphony provides the routine Rsymphony_solve_LP() which interfaces the SYMPHONY solver for mixed integer linear programs. SYMPHONY applies LP relaxation with a branch-and-cut approach. It is part of the Computational Infrastructure for Operations Research (COIN-OR) project which is an initiative to spur the development of open source software for the operations research community. [LP, IP, MILP]
• The CSDP semidefinite programming library is interfaced by package Rcsdp. [SDP]

Interfaces to Commercial Optimizers

This section surveys interfaces to commercial solvers. Typically, the corresponding libraries have to be installed separately.

• Package Rcplex provides an interface to the CPLEX solver package from ILOG . It provides dual/primal simplex optimizers as well as a barrier optimizer for solving large scale linear and quadratic programs. Furthermore, it offers a mixed integer optimizer to solve difficult mixed integer programs. Note that CPLEX is not free and you have to get a license from ILOG . [LP, IP, BP, QP, MILP, MIQP, IPM]

Specific Applications in Optimization

• In package clue solve_LSAP() enables the user to solve the linear sum assignment problem (LSAP) using an efficient C implementation of the Hungarian algorithm. [SPLP]
• Package goalprog provides some functions for lexicographic linear goal programming and optimization. Goal programming is a branch of multi-objective, multi-criteria decision analysis. [MOP]
• Multi-criteria optimization problems can be solved using package mco which implements genetic algorithms. [MOP]
• igraph, a package for graph and network analysis, uses the very fast igraph C library. It can be used to calculate shortest paths, maximal network flows, minimum spanning trees, etc. [GRAPH]
• maxLik adds a likelihood-specific layer on top of a number of maximization routines like Brendt-Hall-Hall-Hausman (BHHH) and Newton-Raphson among others. It includes summary and print methods which extract the standard errors based on the Hessian matrix and allows easy swapping of maximization algorithms.
• Package quantreg contains variations of simplex and of interior point routines ( nlrq(), crq()). It provides an interface to L1 regression in the R code of function rq(). [SPLP, LP, IPM]
• Package optmatch provides routines for solving matching problems by translating them into minimum-cost flow problems, which are in turn solved optimally by the RELAX-IV codes of Bertsekas and Tseng (free for research). [SPLP]
• Package sna contains the function lab.optim() which is the front-end to a series of heuristic routines for optimizing some bivariate graph statistic. [GRAPH]
• Package TSP provides basic infrastructure for handling and solving the traveling salesperson problem (TSP). The main routine solve_TSP() solves the TSP through several heuristics. In addition, it provides an interface to the Concorde TSP Solver , which has to be downloaded separately. [SPLP]

Classification According to Subject

What follows is an attempt to provide a by-subject overview of packages. The full name of the subject as well as the corresponding MSC code (if available) are given in brackets.

• LP (Linear programming, 90C05): boot, glpk, limSolve, linprog, lpSolve, lpSolveAPI, rcdd, Rcplex, Rglpk, Rsymphony, quantreg
• GO (Global Optimization): Rdonlp2
• SPLP (Special problems of linear programming like transportation, multi-index, etc., 90C08): clue, lpSolve, lpSolveAPI, optmatch, quantreg, TSP
• BP (Boolean programming, 90C09): glpk, Rglpk, lpSolve, lpSolveAPI, Rcplex
• IP (Integer programming, 90C10): glpk, lpSolve, lpSolveAPI, Rcplex, Rglpk, Rsymphony
• MIP (Mixed integer programming and its variants MILP for LP and MIQP for QP, 90C11): glpk, lpSolve, lpSolveAPI, Rcplex, Rglpk, Rsymphony
• SP (Stochastic programming, 90C15): stoprog
• QP (Quadratic programming, 90C20): kernlab, limSolve, LowRankQP, quadprog, Rcplex
• SDP (Semidefinite programming, 90C22): Rcsdp
• MOP (Multi-objective and goal programming, 90C29): goalprog, mco
• NLP (Nonlinear programming, 90C30): Rdonlp2
• GRAPH (Programming involving graphs or networks, 90C35): igraph, sna
• IPM (Interior-point methods, 90C51): kernlab, glpk, LowRankQP, quantreg, Rcplex
• RGA (Methods of reduced gradient type, 90C52): stats ( optim()), gsl
• QN (Methods of quasi-Newton type, 90C53): stats ( optim()), gsl, ucminf