modeling languages

Detection and Transformation of Second-Order Cone Programming Problems in a General-Purpose Algebraic Modeling Language

  • Jared Erickson
  • Robert Fourer
    • Categories Modeling Languages and Systems, Second-Order Cone Programming Tags , ,

    Diverse forms of nonlinear optimization problems can be recast to the special form of second-order cone problems (SOCPs), permitting a wider variety of highly effective solvers to be applied. Popular solvers assume, however, that the necessary transformations to required canonical forms have already been identified and carried out. We describe a general approach to the … 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

    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

    Kestrel: An Interface from Optimization Modeling Systems to the NEOS Server

  • Elizabeth D. Dolan
  • Robert Fourer
  • Jean-Pierre Goux
  • Todd S. Munson
  • Jason Sarich
    • Categories Modeling Languages and Systems, Optimization Software and Modeling Systems, Optimization Software Design Principles Tags , , ,

    The NEOS Server provides access to a variety of optimization resources via the Internet. The new Kestrel interface to the Server enables local modeling environments to request NEOS optimization services and retrieve the results for local visualization and analysis, so that users have the same convenient access to remote NEOS solvers as to those installed … Read more

    LPFML: A W3C XML Schema for Linear and Integer Programming

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

    There are numerous algebraic modeling languages for generating linear programs and numerous solvers for computing solutions to linear programs. This proliferation of modeling languages and solvers is frustrating to modelers who find that only certain languages connect to certain solvers. One way to encourage modeler-solver compatibility is to use a standard representation of a problem … Read more

    Numerical Issues and Influences in the Design of Algebraic Modeling Languages for Optimization

  • Robert Fourer
  • David M. Gay
    • Categories Complementarity and Variational Inequalities, Modeling Languages and Systems, Optimization Software Design Principles Tags , , , , ,

    This paper draws from our experience in developing the AMPL modeling language, to show where numerical issues have been crucial to modeling language design and where modeling language advances have strongly influenced the design of solvers. CitationProceedings of the 20th Biennial Conference on Numerical Analysis, Dundee, Scotland, D.F. Griffiths and G.A. Watson, eds., University of … Read more

    Extending an Algebraic Modeling Language to Support Constraint Programming

  • Robert Fourer
  • David M. Gay
    • Categories Combinatorial Optimization, Modeling Languages and Systems Tags ,

    We describe extensions to algebraic modeling languages and their solver interfaces that will be needed to take advantage of constraint programming solvers, particularly in the area of combinatorial optimization. CitationTechnical Report, Department of Industrial Engineering and Management Sciences, Northwestern University (2001); based on a shorter version that appeared in the Proceedings of the Third International … Read more