IPOPT
Encyclopedia
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in Fortran
and C
and is released under the EPL
(formerly CPL
). IPOPT implements a primal-dual interior point method
, and uses line searches based on Filter methods (Fletcher and Leyffer). IPOPT can be called from various modeling environments and C
.
IPOPT is part of the COIN-OR
project.
IPOPT is designed to exploit 1st and 2nd derivative (Hessians
) information if provided (usually via automatic differentiation
routines in modeling environments such as AMPL
). If no Hessians are provided, IPOPT will approximate them using a quasi-Newton method
s, specifically a BFGS update
.
It was originally developed by Andreas Wächter, a former Ph.D.
student in department of chemical engineering
at Carnegie Mellon University
, under the supervision of Lorenz T. Biegler.
Arvind Raghunathan later created an extension to IPOPT for Mathematical programming with equilibrium constraints
(MPEC) http://epubs.siam.org/sam-bin/getfile/SIOPT/articles/42908.pdf. This version of IPOPT is generally known as IPOPT-C (with the 'C' standing for 'complementarity'). While in theory any mixed-integer program can be recast as an MPEC, it may or may not be solvable with IPOPT-C. Solution of MINLPs (Mixed-Integer Nonlinear Programs) using IPOPT is still being explored http://egon.cheme.cmu.edu/IBM/page.htm https://projects.coin-or.org/Bonmin.
Carl Laird and Andreas Wächter are the developers of IPOPT 3.0, which is a re-implementation of IPOPT in C++
.
Fortran
Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...
and 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....
and is released under the EPL
Eclipse Public License
The Eclipse Public License is an open source software license used by the Eclipse Foundation for its software. It replaces the Common Public License and removes certain terms relating to litigations related to patents....
(formerly CPL
Common Public License
In computing, the CPL is a free software / open-source software license published by IBM. The Free Software Foundation and Open Source Initiative have approved the license terms of the CPL....
). IPOPT implements a primal-dual interior point method
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...
, and uses line searches based on Filter methods (Fletcher and Leyffer). IPOPT can be called from various modeling environments and 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....
.
IPOPT is part of the COIN-OR
COIN-OR
COIN-OR, which stands for Computational Infrastructure for Operations Research, is a project that aims to "create for mathematical software what the open literature is for mathematical theory." The open literature provides the OR community with a peer-review process and an archive...
project.
IPOPT is designed to exploit 1st and 2nd derivative (Hessians
Hessian matrix
In mathematics, the Hessian matrix is the square matrix of second-order partial derivatives of a function; that is, it describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named...
) information if provided (usually via automatic differentiation
Automatic differentiation
In mathematics and computer algebra, automatic differentiation , sometimes alternatively called algorithmic differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program...
routines in modeling environments such as 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...
). If no Hessians are provided, IPOPT will approximate them using a quasi-Newton method
Quasi-Newton method
In optimization, quasi-Newton methods are algorithms for finding local maxima and minima of functions. Quasi-Newton methods are based on...
s, specifically a BFGS update
BFGS method
In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno method is a method for solving nonlinear optimization problems ....
.
It was originally developed by Andreas Wächter, a former Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
student in department of chemical engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...
at Carnegie Mellon University
Carnegie Mellon University
Carnegie Mellon University is a private research university in Pittsburgh, Pennsylvania, United States....
, under the supervision of Lorenz T. Biegler.
Arvind Raghunathan later created an extension to IPOPT for Mathematical programming with equilibrium constraints
Mathematical programming with equilibrium constraints
Mathematical programming with equilibrium constraints is the study ofconstrained optimization problems where the constraints include variational inequalities or complementarities...
(MPEC) http://epubs.siam.org/sam-bin/getfile/SIOPT/articles/42908.pdf. This version of IPOPT is generally known as IPOPT-C (with the 'C' standing for 'complementarity'). While in theory any mixed-integer program can be recast as an MPEC, it may or may not be solvable with IPOPT-C. Solution of MINLPs (Mixed-Integer Nonlinear Programs) using IPOPT is still being explored http://egon.cheme.cmu.edu/IBM/page.htm https://projects.coin-or.org/Bonmin.
Carl Laird and Andreas Wächter are the developers of IPOPT 3.0, which is a re-implementation of IPOPT in 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...
.
External links
- IPOPT home page
- IPOPT is supported in AIMMSAIMMSAIMMS is a software system designed for modeling and solving large-scale optimization and scheduling-type problems....
, AMPLAMPLAMPL, 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...
, APMonitorAPMonitorAPMonitor, or "Advanced Process Monitor", is a modeling language for differential and algebraic equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic...
, GAMSGeneral Algebraic Modeling SystemThe 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...
, MATLABMATLABMATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
and OpenOptOpenOptOpenOpt is an open-source framework for numerical optimization, nonlinear equations and systems of them. It is licensed under the BSD license, making it available to be used in both open- and closed-code software. The package already has some essential ....