Advanced Optimization Capabilities in Mathematica with MathOptimizer Professional
October 28, 2003--MathOptimizer Professional is now available from Wolfram
Research and offers advanced strategies for the solution of global and convex
optimization problems within the Mathematica environment. Developed and
supported by Pintér Consulting Services, Inc. in conjunction with Frank J.
Kampas, MathOptimizer Professional combines the power and rich modeling
capabilities of Mathematica with the established LGO (Lipschitz Global
Optimizer) solver suite, also developed by Janos Pintér of Pintér
Together, these components enable MathOptimizer Professional to provide
sophisticated application development tools and solver functionality. With
applications in numerical mathematics and computer science, advanced
engineering design and operations, chemical and process industries,
econometrics and finance, medical research and biotechnology, and a range of
advanced scientific modeling projects, MathOptimizer Professional is an
extremely versatile and robust package.
MathOptimizer Professional lets users create models in Mathematica and then
automatically translates them into C or Fortran. Next, an external compiler
links to LGO, which solves the optimization model, and the results are
seamlessly reported back to Mathematica. Except for issuing a calling statement
from Mathematica, the user does not have to work directly with the compiler or LGO.
The LGO solver suite integrates the following optimization strategies:
- Branch-and-bound-based (adaptive partition and sampling) global search
- Adaptive stochastic global search
- Adaptive stochastic multistart-based global search
- Bound-constrained local search based on the use of an exact penalty function
- Constrained local search based on a generalized reduced gradient approach
Using LGO solver technology, MathOptimizer Professional can handle complex,
large-scale models with up to one thousand variables and one thousand constraints. 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 may contact
the developers directly to relax these limitations without additional fees, but all related
in-depth product support is subject to a consulting agreement between the client and
Users should note that MathOptimizer Professional is not an update to the
MathOptimizer application package, which is also developed by Pintér
Consulting and available from Wolfram Research. Although the two products
solve similar optimization problems, they employ different algorithms and
methods. MathOptimizer is a native Mathematica application that can be used
on all optimization models formulated in Mathematica, whereas
MathOptimizer Professional uses a compiler-based solver procedure that is
external to Mathematica, enabling the product to handle those models that
can be directly translated to C or Fortran. Both products will continue to
be supported by the developers to meet a broader range of user needs.
MathOptimizer Professional comes with an extensive user guide that
contains mathematical background notes, modeling tips, test problems, and
many nontrivial examples. Upon installation, the user guide can be accessed directly
through the Mathematica Help Browser.
Professional is available.