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Ziena Knitro

Non-linear optimization problems arise in numerous business and industry applications, such as optimizing a portfolio in the financial industry or getting the optimal pricing in the energy industry. Customers in hundreds of sites worldwide rely on KNITRO to deliver high performing and powerful optimization solutions for the most challenging applications in all industries: financial, energy, communications, science and engineering. KNITRO has been developed by Ziena Optimization.

Ziena was founded in 2001 by world-renowned scientists from Northwestern University to provide superior software tools and responsive professional technical support for difficult non-linear optimization problems. On July 1st 2015, Artelys acquired Ziena Optimization, taking in charge the development of KNITRO in addition to the worldwide distribution and support of the software.

KNITRO is available as a standalone component and with the AMPL modeling environment.


The most advanced optimization techniques

KNITRO is an ideal tool for solving problems, such as pricing or revenue management, parameter identification in financial and industrial models or design and operation of electricity and gas transportation networks. It can efficiently handle non-convex non-linear models with thousands of variables. KNITRO is the first non-linear optimization tool that offers two options for inequality constrained problems: "interior points" and "active set." These options reinforce the efficiency for a wide range of models with multiple structures.

Artelys offers partnership programs with universities, public training and research centers to promote teaching and research in optimization. Academic partners get KNITRO and AMPL licenses at discounted prices.

For further information on academic partnership, please contact us.

Key Features

Think one step ahead and let KNITRO be your competitive advantage!

The optimization techniques used by KNITRO offer the leading combination of computational efficiency and robustness. KNITRO is the only nonlinear solver with four different algorithms, allowing it to solve a large range of complex nonlinear problems.

Key features

• Efficient and robust solution on large scale problems
• Two interior-point/barrier and two active-set/SQP algorithms
• Two algorithms for mixed-integer nonlinear optimization
• Heuristics, cutting planes, branching rules for MINLP
• Parallel multistart feature for global optimization
• Ability to run multiple algorithms concurrently
• Automatic and parallel tuning of option settings
• Automatic computation of approximate first-order and second-order derivatives
• Smart initialization strategies and fast infeasibility detection

New KNITRO 9.1 features

• New SQP algorithm designed for Derivative-Free Optimization
• Simplified option-based derivative checker
• New features in MATLAB:
- Specialized function to solve nonlinear least square models
- Addition of the derivative checker
- Performance and API improvements
• Deterministic parallel multistart
• New interior-point refinement option to improve solution accuracy
• Significant speedups for NLPs, MINLPs, and models with range constraints (24% decrease in CPU time vs KNITRO 9.0)

Problems classes solved by KNITRO

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

Programming interfaces


Modeling language interfaces


Operating Systems

Business & academic applications

KNITRO is currently used in many application areas, thus demonstrating its versatility.

This section details some of the typical applications of KNITRO with references to the academic literature. From fundamental mathematics to sustainable development, KNITRO was found useful by a large range of Operations Research practioners.

Feel free to contact us to receive more information regarding KNITRO and its success stories.


Financial & banking

Typical uses of KNITRO:

• Portfolio optimization with transactions costs
• Optimal pricing and risk management
• Volatility estimation
• Credit risk
• Strategic bidding and auctions (Nash equilibrium)

In the literature:

• Byrd, J. R., and Liu, Z. (2007): "Nonlinear Optimization Methods with Financial Applications", Case Studies in Optimization, Ziena.
• Nocedal, J. (2008): "The ZIENA Solver for American Options Pricing", Case Studies in Optimization, Ziena.


Computational economics & game theory

Typical uses of KNITRO:

• Design of economic policies
• Yield management
• Demand modeling
• Maximum-likelihood estimation
• Nash equilibrium

In the literature:

• Conlon, C. T. (2009): "A Dynamic Model of Costs and Margins in the LCD TV Industry", Unpublished manuscript.
• Hanson, D. A., Kryukov, Y., Leyffer, S., and Munson, T. S. (2009): "Optimal Control Model of Technology Transition", No 2009-E24, GSIA Working Papers from Carnegie Mellon University, Tepper School of Business.
• Dubé, J.-P., Fox, J. T., and Su, C.-L. (2012): "Improving the numerical performance of static and dynamic aggregate discrete choice random coefficients demand estimation", in Econometrica, 80 (5), 2231-2267.
• Egesdal, M., Lai, Z., and Su, C.-L. (2012): "Estimating Dynamic Discrete-Choice Games of Incomplete Information", Working paper.


Statistics & data analysis

Typical uses of KNITRO:

• Nonlinear least squares analysis (regression / data fitting)
• Support vector machines
• Data mining
• Data clustering
• Inference analysis
• Parameter estimation
• Inverse problems

In the literature:

• Wang, G., Zhu, Z., Du, W., and Teng, Z. (2008): "Inference Analysis in Privacy-Preserving Data Re-publishing", Data Mining, 2008, ICDM '08, Eight IEEE International, 1079-1084.
• Fuchs, M., and Neumaier, A. (2010): "Optimization in latent class analysis", Technical Report TR/PA/10/89, CERFACS.
• Rauchs, G., and Dumitriu, D. (2010): "Indentation testing parameter identification using an optimization procedure based on genetic algorithms", in Proc. of the Romanian Academy, Series A: Mathematics, 10 (2), 165-172.



Typical uses of KNITRO:

• Nonlinear (AC) optimal power flow (OPF) problems
• Security-Constrained OPF (SCOPF) problems
• Optimization of generation costs and transmission losses
• Modeling of head effects in the optimal management of water reservoirs Nonlinear OPF (optimal power flow) problem
• Oil & gas production optimization 

In the literature:

• Plantenga, T. (2006): "KNITRO for Nonlinear Optimal Power Flow Applications", Case Studies in Optimization, Ziena.
• Hu, B., Cañizares, C. A., and Liu, M.(2010): "Secondary and Tertiary Voltage Regulation Based on Optimal Power Flows", Bulk Power System Dynamics and Control (iREP) - VIII (iREP), 2010 iREP Symposium, 1-6.
• Gutierrez-Martinez, V. J., Cañizares, C. A., Fuerte-Esquivel, C. R., Pizano-Martinez, A., and Gu, X. (2011): "Neural-Network Security-Boundary Constrained Optimal Power Flow", IEEE Transactions on Power Systems, 26 (1), 63-72.
• Ferreira, E. C., Baptista, E. C., and Soler, E. M. (2012): "An investigation about barrier parameters update strategy and the Optimal Power Flow Solution", EngOpt 2012, 3rd International Conference on Engineering Optimization.)
• Barragan Hernandez, A., Vazquez-Roman, R., Rosales-Marines, L., Garcia-Sanchez, F. : "A strategy for simulation and optimization of gas and oil production", Computers and Chemical Engineering 30, 2005, 215–227


Sustainable development

Typical uses of KNITRO:

• Virtual population analysis
• Population growth management
• Transition path control

In the literature:

• Tahvonen, O. (2008): "Optimal harvesting of age-structured fish populations", CEMARE Research Paper, P165.
• Tahvonen, O., Pukkala, T., Laiho, O., Lähde, E., and Niinimäki, S. (2010): "Optimal management of uneven-aged Norway spruce stands", in Forest Ecology and Management, 260 (1), 106-115.


Optimal control & dynamic optimization

Typical uses of KNITRO:

• Trajectory optimization
• Optimization with partial differential equations
• PDE-Constrained optimization with discrete decisions
• Variational Analysis

In the literature:

• Abdallah, L., Haddou, M., and Khardi, S. (2010): "Optimization of operational aircraft parameters reducing noise emission", in Applied Mathematical Sciences, 4 (11), 515-535.
• Nahayo, F., Khardi, S., Ndimubandi, J., Haddou, M., and Hamadiche, M. (2010): "Two-Aircraft Acoustic Optimal Control Problem: SQP algorithms", in ARIMA, 14, 101-123.
• You, F., and Leyffer, S. (2011): "Mixed-Integer Dynamic Optimization for Oil-Spill Response Planning with Integration of a Dynamic Oil Weathering Model", in AIChE Journal, 57 (12), 3555-3564.



Typical uses of KNITRO:

• Transmission network optimization
• Resource allocation

In the literature:

• Sosa-Paz, C., Ruckmann, J., and Sánchez-Meraz, M. (2010): "Joint Routing, Link Scheduling and Power Control for Wireless Multi-hop Networks for CDMA/TDMA Systems", in Científica, 14 (4), 165-172.


Optics & spectroscopy

Typical uses of KNITRO:

• Light polarization control
• Isomer conformational analysis

In the literature:

• Lott, G. A., Perdomo-Ortiz, A., Utterback, J. K., Widom, J. R., Aspuru-Guzikb, A., and Marcus, A. H. (2011): "Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2D fluorescence spectroscopy", in Proceedings of the National Academy of Sciences, 108 (40), 16521-16526.
• Tripathi, S., Paxman, R., Bifano, T., and Toussaint, K. C. Jr. (2012): "Vector transmission matrix for the polarization behavior of light propagation in highly scattering media", in Optics Express, 20 (14), 16067-16076.


Mathematics & geometry

Typical uses of KNITRO:

• Shape curvature minimization via contour regularization
• Independent proof check
• Counterexample detection

In the literature:

• Hales, T. C., and McLaughlin, S. (2010): "The dodecahedral conjecture", in Journal of the american mathematical society, 23 (2), 299-344.
• Bretin, E., Lachaud, J.-O., and Oudet, E. (2011): "Regularization of discrete contour by Willmore energy", in Journal of mathematical imaging and vision, 40 (2), 214-229.

KNITRO documentation

KNITRO 9.1 installation, user, and reference guides are provided in the User's Manual:

Online documentation - KNITRO 9.1, December 2014

Older releases:

• KNITRO 9.0


Ziena License Manager documentation

Ziena License Manager 9.0


KNITRO licensing

KNITRO Commercial Licensing
KNITRO Academic Licensing
KNITRO End-User License Agreement

Téléchargement d’une version d’essai

step 1Sélectionnez une version

  • Version destinée aux étudiants souhaitant utiliser KNITRO dans le cadre de leurs études.

  • Version destinée aux entreprises souhaitant évaluer les performances de KNITRO Aucune utilisation commerciale de cette version n’est autorisée.

  • Version destinée aux enseignants-chercheurs souhaitant évaluer KNITRO dans le cadre d’un projet de recherche publique ou pour la préparation d’un cours.


step 2Version étudiante

Version d’évaluation limitant la taille du problème à 300 variables et 300 contraintes, valable 6 mois

En téléchargeant ou en utilisant ce composant, j’accepte les conditions suivantes :

• utilisation à des fins d’étude
• aucune utilisation à des fins commerciales
• uniquement durant la période d’évaluation


step 2Version commerciale

Version complète valable 1 mois

En téléchargeant ou en utilisant ce composant, j’accepte les conditions suivantes :

• uniquement à des fins d’évaluation
• aucune utilisation à des fins commerciales
• uniquement durant la période d’évaluation


step 2Version académique

Merci de préciser votre choix :

• Version limitant la taille du problème (300 variables et 300 contraintes), valable 6 mois*

• Version complète valable 1 mois*

Je comprends que cette version est destinée aux professionels de l’éducation à des fins d’enseignement. En téléchargeant ou en utilisant ce composant, j’accepte les conditions suivantes :

• uniquement à des fins d’enseignement
• aucune utilisation à des fins commerciales
• uniquement durant la période d’évaluation

Comment obtenir l’ID de votre ordinateur ?


step 3Contrat de licence

J’ai lu et j’accepte le contrat de licence.

Frequently asked questions

This section has a selection of general issues encountered during the installation and the use of KNITRO and our answers to help you. For specific help, please contact us.

Q : What should I do to purchase KNITRO?
A : Please contact KNITRO sales team.

Q: What should I do when I have difficulties installing KNITRO?
A: Read sections Installation and Troubleshooting of the user manual. If you cannot resolve your problem, please contact KNITRO support team (for users under maintenance only).

Q: What should I do to make KNITRO solve my problem faster?
A: Read section Tips and Tricks of the user manual. If you cannot resolve your problem, please contact KNITRO support team (for users under maintenance only).

Q : Where can I discuss with the KNITRO community?
A : The KNITRO forum is hosted by a Google group. You can refer to the KNITRO community to discuss about KNITRO, provide feedbacks, ask technical questions, etc.

KNITRO support

Artelys provides worlwide technical support and assistance for KNITRO.

More information