KNITRO
Encyclopedia
KNITRO is a software package
for solving large scale mathematical optimization
problems. KNITRO is specialized for nonlinear optimization, but also solves linear programming
problems, quadratic programming
problems, and systems of nonlinear equations
. The unknowns in these problems must be continuous variables in continuous functions; however, functions can be convex or nonconvex. KNITRO computes a numerical solution to the problem -- it does not find a symbolic mathematical
solution.
KNITRO can also solve mixed integer linear, quadratic or nonlinear programming problems, i.e. problems with variables that take integer values.
Optimization problems must be presented to KNITRO in mathematical form, and should provide a way of computing function derivatives using sparse matrices
. Problems may be written in C
, C++
, Fortran
, or Java
, in which case KNITRO is called as a software routine to solve the problem. An often easier approach is to develop the optimization problem in an algebraic modeling language
(AML) like AIMMS
, AMPL
, GAMS
, Mathematica
, etc. The modeling environment computes function derivatives, and KNITRO is called as a "solver" from within the environment.
KNITRO offers three different optimization algorithm
s for solving optimization problems. Two algorithms are of the interior point
type, and one is of the active set type. These algorithms are known to have fundamentally different characteristics; for example, interior point methods follow a path through the interior of the feasible region while active set methods tend to stay at the boundaries. KNITRO provides both types of algorithm for greater flexibility in solving problems, and allows crossover during the solution process from one algorithm to another. The code also provides a multistart option for promoting the computation of the global minimum.
KNITRO, short for "Nonlinear Interior point Trust Region Optimization" (the "K" is silent) was created primarily by Richard Waltz, Jorge Nocedal, Todd Plantenga and Richard Byrd. It is produced by Ziena Optimization, Inc. KNITRO was introduced in 2001 as a derivative of academic research at Northwestern, and has undergone continual improvement since.
Software package (installation)
In package management systems, which are commonly used with Linux-based operating systems, a package is a specific piece of software which the system can install and uninstall....
for solving large scale mathematical optimization
Mathematical Programming
Mathematical Programming, established in 1971, and published by Springer Science+Business Media, is the official scientific journal of the Mathematical Optimization Society. It currently consists of two series: A and B. The "A" series contains general publications. The "B" series focuses on topical...
problems. KNITRO is specialized for nonlinear optimization, but also solves linear programming
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
problems, quadratic programming
Quadratic programming
Quadratic programming is a special type of mathematical optimization problem. It is the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables....
problems, and systems of nonlinear equations
Simultaneous equations
In mathematics, simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations...
. The unknowns in these problems must be continuous variables in continuous functions; however, functions can be convex or nonconvex. KNITRO computes a numerical solution to the problem -- it does not find a symbolic mathematical
Symbolic computation
Symbolic computation or algebraic computation, relates to the use of machines, such as computers, to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols...
solution.
KNITRO can also solve mixed integer linear, quadratic or nonlinear programming problems, i.e. problems with variables that take integer values.
Optimization problems must be presented to KNITRO in mathematical form, and should provide a way of computing function derivatives using sparse matrices
Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....
. Problems may be written in C
C (programming language)
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
, C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
, Fortran
Fortran
Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...
, or Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
, in which case KNITRO is called as a software routine to solve the problem. An often easier approach is to develop the optimization problem in an algebraic modeling language
Algebraic modeling language
Algebraic Modeling Languages are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation...
(AML) like AIMMS
AIMMS
AIMMS is a software system designed for modeling and solving large-scale optimization and scheduling-type problems....
, AMPL
AMPL
AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computation AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and...
, GAMS
General Algebraic Modeling System
The General Algebraic Modeling System is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to...
, Mathematica
Mathematica
Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
, etc. The modeling environment computes function derivatives, and KNITRO is called as a "solver" from within the environment.
KNITRO offers three different optimization algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s for solving optimization problems. Two algorithms are of the interior point
Interior point method
Interior point methods are a certain class of algorithms to solve linear and nonlinear convex optimization problems.The interior point method was invented by John von Neumann...
type, and one is of the active set type. These algorithms are known to have fundamentally different characteristics; for example, interior point methods follow a path through the interior of the feasible region while active set methods tend to stay at the boundaries. KNITRO provides both types of algorithm for greater flexibility in solving problems, and allows crossover during the solution process from one algorithm to another. The code also provides a multistart option for promoting the computation of the global minimum.
KNITRO, short for "Nonlinear Interior point Trust Region Optimization" (the "K" is silent) was created primarily by Richard Waltz, Jorge Nocedal, Todd Plantenga and Richard Byrd. It is produced by Ziena Optimization, Inc. KNITRO was introduced in 2001 as a derivative of academic research at Northwestern, and has undergone continual improvement since.
External links
- KNITRO (Ziena home page)
- Jorge Nocedal (home page at Northwestern University)
- KNITRO is supported in the AIMMS, AMPL, Frontline (Excel), GAMS, Mathematica and MPL Modeling Systems
- Artelys (Worldwide distributor)
- TOMLAB makes KNITRO available to Matlab users (From Matlab R2008A, KNITRO is also directly available through the Optimization Toolbox)