MathOptimizer Professional 2.1
Advanced Global and Local Nonlinear Optimization
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 x D Rn D:={x:
xl xxu g(x)0}
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| 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 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 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.
Note: Contact the developer for upgrade or trial
information. MathOptimizer Professional 2.1
requires Mathematica 6 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.
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