An Advanced Modeling and Optimization System for Mathematica
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.
Special emphasis is placed on 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 (which are often defined by a complicated, numerically
MathOptimizer 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
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.
About the Developers
János D. Pintér (PhD, DSc) is a researcher and software developer working mostly in the area of nonlinear optimization. He received the 2000 INFORMS Computing Society Prize for Research Excellence for the book Global Optimization in Action, and he has also authored and edited other books and numerous articles related to this field. Dr. Pintér serves on the editorial board of the Journal of Global Optimization and of several professional journals, and currently is Global Optimization Vice Chair of the INFORMS Optimization Society. He is the developer of LGO and of MathOptimizer, a native Mathematica application package for global and local optimization.
Frank J. Kampas (PhD, MBA) has extensive experience related to programming, model development, and optimization in Mathematica and other languages. He has used Mathematica in the solar energy, aerospace, and supply chain management industries and is the developer of MathOptimizer Professional, a link between Mathematica and LGO, as well as co-developer of the most recent version of MathOptimizer.
MathOptimizer is developed and supported by János D. Pintér and Frank J. Kampas.
János D. Pintér, PhD, DSc
Pintér Consulting Services, Inc.
Frank J. Kampas, PhD, MBA
1614 E. Butler Pike
Ambler, Pennsylvania 19002
requires Mathematica 6 or greater and is available for Windows, Linux,
and Mac OS X.