skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

Journal Article · · Mathematical Programming Computation
 [1];  [2];  [2];  [3];  [1]
  1. Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Chemical Engineering
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
  3. Univ. of Wisconsin, Madison, WI (United States). Dept. of Chemical and Biological Engineering
+ Show Author Affiliations

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level 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 high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf 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 state-of-the-art optimization solvers.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC04-94AL85000; KJ0401000; NA0003525
OSTI ID:
1421609
Report Number(s):
SAND-2017-12346J; PII: 127
Journal Information:
Mathematical Programming Computation, Vol. 10, Issue 2; ISSN 1867-2949
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

References (16)

Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems journal October 2008
TACO: a toolkit for AMPL control optimization journal April 2013
Stochastic optimal control model for natural gas networks journal May 2014
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations book January 1998
Efficient parallel solution of large-scale nonlinear dynamic optimization problems journal April 2014
Computing in Operations Research Using Julia journal April 2015
GPOPS-II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming journal October 2014
Pyomo: modeling and solving mathematical programs in Python journal August 2011
Framework in PYOMO for the assessment and implementation of (as)NMPC controllers journal September 2016
A transformation technique for optimal control problems with a state variable inequality constraint journal October 1969
Modeling and optimization with Optimica and JModelica.org—Languages and tools for solving large-scale dynamic optimization problems journal November 2010
A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems * journal July 1984
ACADO toolkit-An open-source framework for automatic control and dynamic optimization journal May 2010
Pyomo – Optimization Modeling in Python book January 2012
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers journal September 2005
Nonlinear Programming book January 2010

Cited By (2)

Dynamic real‐time optimization for a CO 2 capture process journal November 2018
Dynamic optimization for gas blending in pipeline networks with gas interchangeability control journal January 2020

Figures / Tables (7)

Table 1(p. 3)table Table 1
Fig. 1(p. 4)figure Fig. 1
Fig. 2(p. 16)figure Fig. 2
Fig. 3(p. 22)figure Fig. 3
Table 2(p. 24)table Table 2
Table 3(p. 26)table Table 3
Fig. 4(p. 27)figure Fig. 4

Similar Records

Related Subjects

97 MATHEMATICS AND COMPUTING
Dynamic optimization
Mathematical modeling
Algebraic modeling language
DAE constrained optimization
PDE constrained optimization