MathOptimizer

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.

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 intensive procedure).

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 standalone mode.

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 Developer

MathOptimizer is developed and supported by János D. Pintér.

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 his book Global Optimization in Action. He has authored and edited several other books and about 200 other publications related to systems modeling and optimization. Dr. Pintér has served on the editorial board of the Journal of Global Optimization since its 1991 founding, and of the book series SpringerBriefs in Optimization. He is the principal developer of a range of optimization software packages. Dr. Pintér offers consulting services, lectures and training courses focused on computational nonlinear optimization.

János D. Pintér, PhD, DSc
janos.d.pinter@gmail.com

MathOptimizer requires Mathematica 10 or greater and is available for Windows, Linux and macOS.