Advanced Nonlinear Optimization in Mathematica

János D. Pintér
PCS, Inc.
and
Frank J. Kampas
WAM Systems, Inc.

Abstract

In recent years Mathematica’s optimization features have been significantly expanded, both by in-house development and application packages. Such developments make it an increasingly useful tool in advanced modeling and optimization studies. We see particularly strong application potential for Mathematica in nonlinear optimization when the decision model can not be brought to one of the standard model forms, notably, continuous linear programming and its (formally) simplest extensions that include pure and mixed integer linear programming.

In this talk, we review Mathematica’s nonlinear optimization features and—within this context—illustrate the use of our packages MathOptimizer and MathOptimizer Professional. The efficency of these packages is demonstrated by solving uniform and nonuniform circle packing models.