An Advanced Modeling and Optimization System for Mathematica Users

MathOptimizer enables the global and local numerical solution of a very general class of optimization problems defined by a finite number of real-valued, continuous functions over a finite n-dimensional interval region.

A special emphasis is placed upon nonlinear models, including those that typically have an unknown number of local optima. Nonlinear and global optimization problems are ubiquitous in the sciences, engineering, and economics. Several prominent examples are systems of nonlinear equations and inequalities, nonlinear regression, forecasting models, data classification, minimal energy models, various packing problems, risk management and other stochastic decision problems, and the design and operation of "black box" engineering systems (possibly defined by a complicated, numerically intensive procedure).

MathOptimizer currently consists of two core solver packages and a solver integrator package. The first core solver package is used for approximate global optimization of an aggregated merit (exact penalty) function on a given interval range. This package is based on a globally convergent adaptive stochastic search procedure, and it also incorporates statistical estimation techniques.

The second core solver package is meant for precise local optimization. It is based on the standard nonlinear (convex) programming approach and refines a given initial solution. The solver integrator package supports the individual or combined use of the core solver packages, but both of the core packages can also be used in stand-alone mode. Further solver modules are under development and will be made available soon.

The MathOptimizer User Guide includes concise mathematical background notes and useful modeling tips. It also discusses a number of test problems and several nontrivial application examples. The guide can be accessed directly through Mathematica's online help system.

MathOptimizer Licensing
Professional licenses are available, and professional users are entitled to quantity discounts. Fully functional versions with educational and nonprofit research discounts are offered to professors and their students and to qualifying researchers. In addition, individual instructor and student licenses as well as department and site licenses are available.

Product Development and Support
János D. Pintér, the developer of MathOptimizer, is a professional software developer and an active researcher in the area of global/nonlinear optimization. He received the 2000 INFORMS Computing Society Prize for the book Global Optimization in Action and has authored and edited other books and numerous research articles related to this field. Dr. Pintér has served on the editorial board of the Journal of Global Optimization since its founding, and he wrote the chapter titled "Global Optimization: Software, Test Problems, and Applications" for Volume 2 of the Handbook of Global Optimization.

Developed and supported by Pintér Consulting Services, Inc.

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