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词条 Artelys Knitro
释义

  1. Problem classes solved by Artelys Knitro

  2. Algorithms

     NonLinear Programming (NLP) solver  Mixed-Integer NonLinear Programming (MINLP) solver 

  3. Features

  4. References

  5. External links

{{Infobox programming language
| name = Artelys Knitro
| designer = {{ubl|Richard Waltz|Jorge Nocedal|Todd Plantenga|Richard Byrd}}
| developer = Artelys
| license = Proprietary
| website = {{URL|https://www.artelys.com/en/optimization-tools/knitro|Artelys Knitro}}
| year = {{Start date|2001}}
| latest_release_version = 11.1
| latest_release_date = {{Start date and age|2018|11|01}}
| operating_system = Cross-platform
| genre = Algebraic Modeling Language (AML)
}}

Artelys Knitro [1] is a commercial software package for solving large scale nonlinear mathematical optimization problems.

KNITRO – (the original solver name) short for "Nonlinear Interior point Trust Region Optimization" (the "K" is silent) – was co-created by Richard Waltz, Jorge Nocedal, Todd Plantenga and Richard Byrd. It was first introduced in 2001, as a derivative of academic research at Northwestern University (through Ziena Optimization LLC), and has since been continually improved by developers at Artelys.

Optimization problems must be presented to Knitro in mathematical form, and should provide a way of computing function derivatives using sparse matrices (Knitro can compute derivatives approximation but in most cases providing the exact derivatives is beneficial). An often easier approach is to develop the optimization problem in an algebraic modeling language. The modeling environment computes function derivatives, and Knitro is called as a "solver" from within the environment.

Problem classes solved by Artelys Knitro

Knitro is specialized for nonlinear optimization but also solves a wide range of optimization problems:

  • General nonlinear problems (NLP), including non-convex
  • Systems of nonlinear equations
  • Linear problems (LP)
  • Quadratic problems (QP/QCQP/SOCP), both convex and non-convex
  • Least squares problems / regression, both linear and nonlinear
  • Mathematical programs with complementarity constraints (MPCC/MPEC)
  • Mixed-integer nonlinear problems (MIP/MINLP)
  • Derivative-free optimization problems (DFO)

Algorithms

Artelys Knitro contains a wide range of optimization algorithms.

NonLinear Programming (NLP) solver

Knitro offers four different optimization algorithms for solving optimization problems[2]. Two algorithms are of the interior point type, and two are 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.

  • Interior/Direct algorithm
  • Interior/Conjugate Gradient algorithm
  • Active Set algorithm
  • Sequential Quadratic Programming (SQP) algorithm

Mixed-Integer NonLinear Programming (MINLP) solver

Knitro provides tools for solving optimization models (both linear and nonlinear) with binary or integer variables. The Knitro mixed integer programming (MIP) code offers three algorithms for mixed-integer nonlinear programming (MINLP)[3]:

  • Nonlinear Branch and Bound
  • Quesada Grossman algorithm
  • Mixed-Integer Sequential Quadratic Programming (MISQP)

Features

Artelys Knitro supports a variety of programming and modeling languages including[4].

  • Object-oriented interfaces for C++, C#, Java and Python
  • Matrix-oriented interfaces for C, Fortran, MATLAB, and R
  • Links to modeling languages: AIMMS, AMPL, GAMS, and MPL
  • Links to Excel through Frontline Solvers

Artelys Knitro also includes a number of key features:

  • A large set of well-documented user options[5] and automatic tuner
  • (Parallel) multi-start for global optimization
  • Derivatives approximation and checker
  • Internal presolver

References

  • {{cite book |last=Nocedal |first=Jorge |last2=Wright |first2=Stephen J. |title=Numerical Optimization |edition=2nd |date=2006 |publisher=Springer Publishing |isbn=0-387-30303-0}}
  • {{cite journal |last=Byrd |first=Richard H. |last2=Nocedal |first2=Jorge |last3=Waltz |first3=Richard A. |date=2006 |title=Knitro: An Integrated Package for Nonlinear Optimization |url=https://www.artelys.com/downloads/pdf/composants-numeriques/knitro/papers/integratedpackage.pdf |format=PDF |accessdate=November 17, 2017}}

External links

1. ^[https://www.artelys.com/en/optimization-tools/knitro Artelys Knitro Website]
2. ^[https://www.artelys.com/tools/knitro_doc/2_userGuide/algorithms.html Artelys Knitro NLP algorithms]
3. ^[https://www.artelys.com/tools/knitro_doc/2_userGuide/minlp.html Artelys Knitro MINLP algorithms]
4. ^[https://www.artelys.com/en/optimization-tools/knitro#features-tab Artelys Knitro Features]
5. ^[https://www.artelys.com/tools/knitro_doc/ Artelys Knitro User's Manual]
  • Jorge Nocedal, profile at EECS department of McCormick School of Engineering
{{Mathematical optimization software}}

2 : Numerical software|Mathematical optimization software

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