A structure conveying parallelizable modeling language for mathematical programming

Abstract

Modeling languages are an important tool for the formulation of mathematical programming problems. Many real-life mathematical programming problems are of sizes that make their solution by parallel techniques the only viable option. Increasingly, even their generation by a modeling language cannot be achieved on a single processor. Surprisingly, however, there has been no effort so far at the development of a parallelizable modeling language. We present a modeling language that enables the modular formulation of optimization problems. Apart from often being more natural for the modeler, this enables the parallelization of the problem generation process making the modeling and solution of truly large problems feasible. The proposed structured modeling language is based on the popular modeling language AMPL and implemented as a pre-/postprocessor to AMPL. Unlike traditional modeling languages, it does not scramble the block-structure of the problem but passes this on to the solver if wished. Solvers such as block linear algebra exploiting interior point solvers and decomposition solvers can therefore directly exploit the structure of the problem.