Modeling Languages and Systems

A Collection of 1,300 Dynamical Systems for Testing Data Fitting, Optimal Control, Experimental Design, Identification, Simulation or Similar Software – User’s Guide

  • Klaus Schittkowski
    • Categories Modeling Languages and Systems, Optimization Software Benchmark, Systems governed by Differential Equations Optimization

    We describe a collection of test problems which have been used to develop and test data fitting software for identifying parameters in explicit model functions, dynamical systems of equations, Laplace transformations, systems of ordinary differential equations, differential algebraic equations, or systems of one-dimensional time-dependent partial differential equations with or without algebraic equations. The test cases … Read more

    Code verification by static analysis: a mathematical programming approach

  • Stephane Le Roux
  • Leo Liberti
  • Fabrizio Marinelli
  • Jeremy Leconte
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Modeling Languages and Systems Tags , , , , ,

    Automatic verification of computer code is of paramount importance in embedded systems supplying essential services. One of the most important verification techniques is static code analysis by abstract interpretation: the concrete semantics of a programming language (i.e.the values $\chi$ that variable symbols {\tt x} appearing in a program can take during its execution) are replaced … Read more

    Robust Optimization Made Easy with ROME

  • Joel Goh
  • Melvyn Sim
    • Categories Modeling Languages and Systems, Robust Optimization Tags ,

    We introduce an algebraic modeling language, named ROME, for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically meaningful way. In this paper, we highlight key features of ROME which expediates the modeling and subsequent … Read more

    A Structure-Conveying Modelling Language for Mathematical and Stochastic Programming

  • Marco Colombo
  • Jacek Gondzio
  • Andreas Grothey
  • Jonathan Hogg
  • Kristian Woodsend
    • Categories Modeling Languages and Systems Tags , , ,

    We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to onstruct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the … Read more

    Python Optimization Modeling Objects (Pyomo)

  • William E. Hart
    • Categories Modeling Languages and Systems, Optimization Software Design Principles Tags , , ,

    We describe Pyomo, an open-source tool for modeling optimization applications in Python. Pyomo can be used to define abstract problems, create concrete problem instances, and solve these instances with standard solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages like AMPL and GAMS. Pyomo leverages the capabilities of the Coopr software, … Read more

    LIBOPT – An environment for testing solvers on heterogeneous collections of problems – The manual, version 2.0

  • Jean Charles Gilbert
  • Xavier Jonsson
    • Categories Modeling Languages and Systems, Optimization Software Benchmark Tags

    The Libopt environment is both a methodology and a set of tools that can be used for testing, comparing, and profiling solvers on problems belonging to various collections. These collections can be heterogeneous in the sense that their problems can have common features that differ from one collection to the other. Libopt brings a unified … Read more

    Graph Implementations for Nonsmooth Convex Programs

  • Stephen Boyd
  • Michael Grant
    • Categories Convex Optimization, Modeling Languages and Systems, Nonsmooth Optimization Tags , ,

    We describe graph implementations, a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework. This simple and natural idea allows a very wide variety of smooth and nonsmooth convex programs to be easily specified and efficiently solved, using interior-point methods for smooth or cone convex programs. CitationTo … Read more

    LIBOPT – An environment for testing solvers on heterogeneous collections of problems

  • Jean Charles Gilbert
  • Xavier Jonsson
    • Categories Modeling Languages and Systems, Optimization Software Benchmark Tags

    The Libopt environment is both a methodology and a set of tools that can be used for testing, comparing, and profiling solvers on problems belonging to various collections. These collections can be heterogeneous in the sense that their problems can have common features that differ from one collection to the other. Libopt brings a unified … Read more

    Extending Algebraic Modelling Languages for Stochastic Programming

  • Robert Fourer
  • Gautam Mitra
  • Mustapha Sadki
  • Christian Valente
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags

    Algebraic modelling languages have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages by constructing their deterministic equivalent. Unfortunately, this leads to very large model data instances. We propose a direct approach in which the random values of the … Read more

    StAMPL: A Filtration-Oriented Modeling Tool for Stochastic Programming

  • Robert Fourer
  • Leonardo B. Lopes
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags , ,

    Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. To experiment … Read more