The objective of global optimization (GO) is to find the best solution of nonlinear decision models that often have a multitude of global and local optima. GO is of great theoretical and practical importance, with significant applications in mathematics and computer science, natural sciences and engineering, econometrics and finances.
The LGO (Lipschitz Global Optimizer) software serves to solve nonlinear optimization models, using a robust and efficient suite of global and local search algorithms. LGO has been developed and maintained for over a decade, and is discussed in details elsewhere: consult, for instance, Pintér (1996, 1999, 2001a, 2002a), or the peer review by Benson and Sun (2000).
MathOptimizer (Pintér, 2002b) is a recently introduced native Mathematica software product that serves to solve nonlinear optimization models. Kampas and Pintér (2002) solve illustrative, yet non-trivial configuration design models using MathOptimizer. The Developer Conference presentation of Pintér and Purcell (2003) discusses an advanced engineering application solved by MathOptimizer.
Both LGO and MathOptimizer are used worldwide by a growing clientele from education, academic research, consulting, and industry.
Our new product, MathOptimizer Professional (MOP) combines the power of Mathematica with the external LGO solver suite. This results in enhanced solver capabilities, and a performance that is competitive with compiler-based solver implementations.
In this brief article, we review the key features of MOP, and illustrate its capabilites by solving a few global optimization test examples and more difficult challenges. More details and practically motivated examples are discussed in the MathOptimizer Professional User Guide (Pintér and Kampas, 2003).
A talk entitled "Optimization of finite element models with MathOptimizer and ModelMaker" is available here as the download devcon2003.nb.zip, below.