A Structure-Exploiting Tool in Algebraic Modeling Languages

Fragnière, Emmanuel; Gondzio, Jacek; Sarkissian, Robert; Vial, Jean–Philippe

doi:10.1287/mnsc.46.8.1145.12026

Cited by 18 publications

(13 citation statements)

References 18 publications

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“…SET [15] offers facilities to declare the structure of a model as a postscript to the problem: an additional structure file defines the blocks making up the structure of the problem and a list of row and column names that make up each block. This approach requires that the full (unstructured) problem be processed first by the modelling language: hence this hampers any potential parallelisation of the model generation.…”

Section: Modelling Approaches To Structured Problemsmentioning

confidence: 99%

A structure-conveying modelling language for mathematical and stochastic programming

et al. 2009

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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 construct 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 problem, and thus it enables the passing of this structure on to the solver. Interior point solvers that exploit block linear algebra and decomposition-based solvers can therefore directly take advantage of the problem's structure. The language contains features to conveniently model stochastic programming problems, although it is designed with a much broader application spectrum. Mathematics Subject Classification (2000)68N15 · 90C06 · 90C15 Supported by: "Conveying structure from modeling language to a solver", Intel Corporation, Santa Clara, USA. M. Colombo was supported by EPSRC grant EP/E036910/1.

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Section: Modelling Approaches To Structured Problemsmentioning

confidence: 99%

A structure-conveying modelling language for mathematical and stochastic programming

et al. 2009

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“…Chapter 2 in this volume) directly from GAMS. Condevaux-Lanloy, Fragnière, and King [8] extend the structure exploiting tool [15] to permit the formulation of the SMPS format from the AML. In their approach the time-related information is retrieved from the core model handled by the AML, and the uncertainty information is loaded directly into the specialized SMPS-based solver outside the AML.…”

Section: Stochastic Programs In Amlsmentioning

confidence: 99%

“…The problem is represented in a compact format close in spirit to SMPS. Stochastic extension [8] of the structure exploiting tool [15] uses the AML to generate the deterministic part of the model in the form of the core and time files in the SMPS format. The information of uncertainty is produced outside the AML and communicated directly to the specialized solver.…”

Section: Communication Between Solver and Amlmentioning

confidence: 99%

7. Stochastic Programming from Modeling Languages

Fragnière¹,

Gondzio²

2005

Applications of Stochastic Programming

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The majority of deterministic mathematical programming problems have a compact formulation in terms of algebraic equations. Therefore they can easily take advantage of the facilities offered by algebraic modeling languages (AMLs). These tools allow expressing models by using convenient mathematical notation (algebraic equations) and translate the models into a form understandable by the solvers for mathematical programs.AMLs provide facility for the management of a mathematical model and its data, and access different general-purpose solvers. The use of AMLs simplifies the process of building the prototype model and in some cases makes it possible to create and maintain even the production version of the model.As presented in other chapters of this book, stochastic programming is needed when exogenous parameters of the mathematical programming problem are random. Dealing with stochasticities in planning is not an easy task. In a standard scenario-by-scenario analysis, the system is optimized for each scenario separately. Varying the scenario hypotheses, we can observe the different optimal responses of the system and delineate the "strong trends''of the future. Indeed, this scenario-by-scenario approach implicitly assumes perfect foresight. The method provides a first-stage decision, which is valid only for the scenario under consideration. Having as many decisions as there are scenarios leaves the decision maker without a clear recommendation. In stochastic programming the whole set of scenarios is combined into an event tree, which describes the unfolding of uncertainties over the period

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“…Recent developments, tend to automatize this process in the case of large scale structured problems, e.g., block angular structures. SET is the acronym of Structure Exploiting Tool [31], a device that is appended to standard algebraic modeling languages and that allows the user to pass the information relative to the structure. The use of a decomposition scheme can be then fully automatized, leaving the user free to use either the standard Kelley-Goldstein-Cheney-Dantzig-Wolfe-Benders scheme or ACCPM.…”

Section: Constructing Oraclesmentioning

confidence: 99%

Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method

Goffin

Vial

2002

Optimization Methods and Software

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107

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We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis that uses the formalism of the theory of self-concordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in-depth analysis of two extensions that are very relevant to practical problems: the case of multiple cuts and the case of deep cuts.We further examine extensions to problems including feasible sets partially described by an explicit barrier function, and to the case of nonlinear cuts. Finally, we review several implementation issues and discuss some applications.

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A Structure-Exploiting Tool in Algebraic Modeling Languages

Cited by 18 publications

References 18 publications

A structure-conveying modelling language for mathematical and stochastic programming

A structure-conveying modelling language for mathematical and stochastic programming

7. Stochastic Programming from Modeling Languages

Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method

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