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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 Consulting.

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 the developers.

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.

More information about MathOptimizer Professional is available.