Expressing special structures in an algebraic modeling language for mathematical programming

A knowledge of the presence of certain special structures can be advantageous in both the formulation and solution of linear programming problems. Thus it is desirable that linear programming software offers the option of specifying such structures explicitly. As a step in this direction, we describe extensions to an algebraic modeling language that encompass piecewise-linear, network and related structures. Our emphasis is on the modeling considerations that motivate these extensions, and on the design issues that arise in integrating these extensions with the general-purpose features of the language. We observe that our extensions sometimes make models faster to translate as well as to solve, and that they permit a ‘column-wise’ formulation of the constraints as an alternative to the ‘row-wise’ formulation most often associated with algebraic languages.