IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a

software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists ...

library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

for large scale

nonlinear optimization In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or sta ...

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 Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1 ...

, and uses line searches based on Filter methods (

Fletcher Fletcher may refer to: People * Fletcher (occupation), a person who fletches arrows, the origin of the surname * Fletcher (singer) (born 1994), American actress and singer-songwriter * Fletcher (surname) * Fletcher (given name) Places United ...

and Leyffer). IPOPT can be called from various modeling environments and C. IPOPT is part of the

COIN-OR Computational Infrastructure for Operations Research (COIN-OR), is a project that aims to "create for mathematical software what the open literature is for mathematical theory." The open literature (e.g., a research journal) provides the operat ...

project. IPOPT is designed to exploit 1st and 2nd derivative ( Hessians) information if provided (usually via

automatic differentiation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techniques to evaluate the derivative of a function ...

routines in modeling environments such as

AMPL AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems). It was developed b ...

). If no Hessians are provided, IPOPT will approximate them using a

quasi-Newton method Quasi-Newton methods are methods used to either find zeroes or local maxima and minima of functions, as an alternative to Newton's method. They can be used if the Jacobian or Hessian is unavailable or is too expensive to compute at every iteration. ...

s, specifically a BFGS update. IPOPT was originally developed by Ph.D. studen
Andreas Wächter
and Prof
Lorenz T. Biegler
of the Department of Chemical Engineering at

Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

. Their work was recognized with th
INFORMS Computing Society Prize
in 2009. Arvind Raghunathan later created an extension to IPOPT for

Mathematical programming with equilibrium constraints Mathematical programming with equilibrium constraints (MPEC) is the study of constrained optimization problems where the constraints include variational inequalities or complementarities. MPEC is related to the Stackelberg game. MPEC is used ...

(MPEC

This version of IPOPT is generally known as IPOPT-C (with the 'C' standing for 'complementarity'). While in theory any Mixed integer programming, 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 explore

Carl Laird
and Andreas Wächter are the developers of IPOPT 3.0, which is a re-implementation of IPOPT in

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

. Wächter and Laird were awarded the 2011

J. H. Wilkinson Prize for Numerical Software The J. H. Wilkinson Prize for Numerical Software is awarded every four years to honor outstanding contributions in the field of numerical software. The award is named to commemorate the outstanding contributions of James H. Wilkinson in the same f ...

for this development.

References

External links

IPOPT home page
Numerical software Mathematical optimization software Optimization algorithms and methods {{Compu-library-stub

See also

References

External links