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MathOptimizer Professional 3

Advanced Global and Local Nonlinear Optimization Using the External LGO Solver Suite

Mathematica 10 compatible MathOptimizer Professional combines the power of Mathematica with the established LGO (Lipschitz Global Optimizer) solver suite, offering sophisticated application development tools and a solver-based functionality comparable to other compiler-based or optimization modeling language-related implementations.

In use since 1990, the LGO solver engine is currently available for professional C and Fortran compiler platforms, with links to Excel and several prominent optimization modeling languages.

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  xelement ofDsubset ofRn  D:={x: xlless than or equal toxless than or equal toxu  g(x)less than or equal to0}

MathOptimizer Professional graphic   Here xelement ofRn is the vector of decision variables (Rn denotes the Euclidean real n-space); f:Rnright arrowR1 is a continuous objective function; Dsubset ofRn 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:Rnright arrowRm. (Obviously, g(x)less than or equal to0 formally covers all cases of g(x)~0, where ~ denotes any of the operators =, less than or equal to, and greater than or equal to.)

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 graphic above, which shows the squared error function related to solving a given pair of transcendental equations as a function of the two unknown arguments.

The current version of MathOptimizer Professional enables users to solve models of up to one thousand variables and one thousand constraints. These limitations should accommodate most applications because, in global and nonlinear optimization, these rather sizable models result in very difficult and processor-intensive calculations (with corresponding run times on state-of-the-art personal computers varying from a few minutes to several hours). Users can contact the developers directly to relax these limitations at no cost.

More information is available on the features page and from the list of references.


About the Developers

MathOptimizer Professional is developed and supported by János D. Pintér and Frank J. Kampas.

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.

János D. Pintér, PhD, DSc
President/Owner
Pintér Consulting Services, Inc.
email: janos.d.pinter@gmail.com
  Frank J. Kampas, PhD, MBA
1614 E. Butler Pike
Ambler, PA 19002
USA
phone: +1-215-646-5228
email: frank@physicistatlarge.com


Note: Contact the developer for upgrade or trial information. MathOptimizer Professional 3 requires Mathematica 6 or greater and a C or Fortran compiler (specified at time of purchase), and is available for Windows. Additional platforms can be made available upon request to the developers.