pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations
Abstract
We describe pyomo.dae, an open source Pythonbased modeling framework that enables highlevel abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with highorder differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform highlevel abstract models into finitedimensional algebraic problems that can be solved with offtheshelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of stateoftheart optimization solvers.
 Authors:

 Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Chemical Engineering
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Center for Computing Research
 Univ. of Wisconsin, Madison, WI (United States). Dept. of Chemical and Biological Engineering
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1421609
 Report Number(s):
 SAND201712346J
Journal ID: ISSN 18672949; PII: 127
 Grant/Contract Number:
 AC0494AL85000; KJ0401000; NA0003525
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Mathematical Programming Computation
 Additional Journal Information:
 Journal Volume: 10; Journal Issue: 2; Journal ID: ISSN 18672949
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Dynamic optimization; Mathematical modeling; Algebraic modeling language; DAE constrained optimization; PDE constrained optimization
Citation Formats
Nicholson, Bethany, Siirola, John D., Watson, JeanPaul, Zavala, Victor M., and Biegler, Lorenz T. pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations. United States: N. p., 2017.
Web. doi:10.1007/s1253201701270.
Nicholson, Bethany, Siirola, John D., Watson, JeanPaul, Zavala, Victor M., & Biegler, Lorenz T. pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations. United States. doi:10.1007/s1253201701270.
Nicholson, Bethany, Siirola, John D., Watson, JeanPaul, Zavala, Victor M., and Biegler, Lorenz T. Wed .
"pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations". United States. doi:10.1007/s1253201701270. https://www.osti.gov/servlets/purl/1421609.
@article{osti_1421609,
title = {pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations},
author = {Nicholson, Bethany and Siirola, John D. and Watson, JeanPaul and Zavala, Victor M. and Biegler, Lorenz T.},
abstractNote = {We describe pyomo.dae, an open source Pythonbased modeling framework that enables highlevel abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with highorder differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform highlevel abstract models into finitedimensional algebraic problems that can be solved with offtheshelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of stateoftheart optimization solvers.},
doi = {10.1007/s1253201701270},
journal = {Mathematical Programming Computation},
number = 2,
volume = 10,
place = {United States},
year = {2017},
month = {12}
}
Figures / Tables:
Works referenced in this record:
Interiorpoint decomposition approaches for parallel solution of largescale nonlinear parameter estimation problems
journal, October 2008
 Zavala, Victor M.; Laird, Carl D.; Biegler, Lorenz T.
 Chemical Engineering Science, Vol. 63, Issue 19
TACO: a toolkit for AMPL control optimization
journal, April 2013
 Kirches, Christian; Leyffer, Sven
 Mathematical Programming Computation, Vol. 5, Issue 3
Stochastic optimal control model for natural gas networks
journal, May 2014
 Zavala, Victor M.
 Computers & Chemical Engineering, Vol. 64
Efficient parallel solution of largescale nonlinear dynamic optimization problems
journal, April 2014
 Word, Daniel P.; Kang, Jia; Akesson, Johan
 Computational Optimization and Applications, Vol. 59, Issue 3
Computing in Operations Research Using Julia
journal, April 2015
 Lubin, Miles; Dunning, Iain
 INFORMS Journal on Computing, Vol. 27, Issue 2
GPOPSII: A MATLAB Software for Solving MultiplePhase Optimal Control Problems Using hpAdaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming
journal, October 2014
 Patterson, Michael A.; Rao, Anil V.
 ACM Transactions on Mathematical Software, Vol. 41, Issue 1
Pyomo: modeling and solving mathematical programs in Python
journal, August 2011
 Hart, William E.; Watson, JeanPaul; Woodruff, David L.
 Mathematical Programming Computation, Vol. 3, Issue 3
Framework in PYOMO for the assessment and implementation of (as)NMPC controllers
journal, September 2016
 Lozano Santamaría, Federico; Gómez, Jorge M.
 Computers & Chemical Engineering, Vol. 92
A transformation technique for optimal control problems with a state variable inequality constraint
journal, October 1969
 Jacobson, D.; Lele, M.
 IEEE Transactions on Automatic Control, Vol. 14, Issue 5
Modeling and optimization with Optimica and JModelica.org—Languages and tools for solving largescale dynamic optimization problems
journal, November 2010
 Åkesson, J.; Årzén, K. E.; Gäfvert, M.
 Computers & Chemical Engineering, Vol. 34, Issue 11
A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems *
journal, July 1984
 Bock, H. G.; Plitt, K. J.
 IFAC Proceedings Volumes, Vol. 17, Issue 2
ACADO toolkitAn opensource framework for automatic control and dynamic optimization
journal, May 2010
 Houska, Boris; Ferreau, Hans Joachim; Diehl, Moritz
 Optimal Control Applications and Methods, Vol. 32, Issue 3
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
journal, September 2005
 Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E.
 ACM Transactions on Mathematical Software, Vol. 31, Issue 3
Figures / Tables found in this record: