MathOptimizer Professional
An Advanced Nonlinear Optimization Environment for Mathematica with an External LGO Solver Link
MathOptimizer Professional enables the global and local solution of a general class of continuous optimization problems. The model form considered is:
min f(x) subject to x
D
Rn D:={x: xl
xxu g(x)0}
Here xRn is the vector of decision variables (Rn denotes the Euclidean real n-space); f:Rn
R1 is a continuous objective function; DRn is the nonempty set of feasible decisions defined by explicit, finite (with respect to components) lower and upper bounds xl and xu and by a collection of continuous constraint functions g:RnRm. (Obviously, g(x)0 formally covers all cases of g(x)~0, where ~ denotes any of the operators =, , and 
.)
These key analytical assumptions guarantee that the model considered has a globally optimal solution. At the same time--without further specific structural assumptions--this model can represent a very difficult numerical challenge because of the possibility of having a disconnected, nonconvex feasible region and a multitude of local optima. For illustration, please see the figure above, which shows the squared error function related to solving a given pair of transcendental equations as a function of the two unknown arguments.
MathOptimizer Professional combines the power of Mathematica with the established LGO (Lipschitz Global Optimizer) solver suite to offer sophisticated application development tools and a solver functionality that is comparable to other compiler-based or optimization modeling language-related implementations.
In use for nearly 15 years, the LGO solver engine is currently available for professional C and Fortran compiler platforms, with links to Excel and several prominent optimization modeling languages.
Documentation
MathOptimizer Professional includes a user guide that contains mathematical background notes, modeling tips, test problems, and an extensive set of nontrivial application examples. After MathOptimizer Professional is installed, the user guide can be accessed directly through the Mathematica Help Browser.
Additional details are presented in the forthcoming book Advanced Optimization with Mathematica: Scientific, Engineering, and Economic Applications as well as in other related publications and software implementations.
Product Development and Support
MathOptimizer Professional is developed and supported by János D. Pintér and Frank J. Kampas.
János D. Pintér is a researcher and software developer 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 has authored and edited other books and numerous articles related to this field. Pintér serves on the editorial board 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 optimization.
Frank J. Kampas is a researcher and senior developer at WAM Systems, inc., where he is responsible for adding optimization capabilities to the company's supply-chain management software. He has extensive experience related to programming, model development, and optimization in Mathematica and other languages. He is the developer of the link between Mathematica and LGO.