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Global Optimization
Fast and Easy Nonlinear Global Optimization

Global Optimization is a package that performs global nonlinear optimization, using Mathematica as an interface for defining the nonlinear system to be solved and for computing function numeric values. Any function computable by Mathematica can be used as input, including degree of fit of a model against data, recursive functions, and simulation models.

The package includes three functions. MultiStartMin is a hill-climbing algorithm that allows constraints. It is designed to be robust to local minima and to handle large problems, even those with more than 100 variables. No derivatives are required, and the function can even be nondifferentiable. Multiple starts allow the user to find multiple minima if they exist.

GlobalMinima solves problems similar to those solved by MultiStartMin but only solves problems with less than 15 variables. This algorithm is based on the identification of feasible points that define the solution set at each iteration. As lower points are found during the grid refinement process, points far from the current optimum are pruned from the solution set. As a result, multiple minima, if they exist, can be found in a single run. The algorithm can also identify optimal regions rather than only single points. These optimal regions might represent the bounds on feasible management strategies that achieve an equivalent result, or they might depict confidence limits for a parameter estimation problem. Nonlinear inequality constraints, which may even define disjunct parameter search spaces, are allowed.

MaxAllocation is designed for allocation problems such as arise in investment, where a fixed amount of money is to be allocated across a series of investment options. Such problems have a single equality constraint and a positivity restriction on all variables. The path-following algorithm used is able to solve this type of problem with high efficiency, leading to the solution of problems with 300 to over 1,000 variables.

Global Optimization requires Mathematica 3 or later and is available for Windows 95/98/NT, Macintosh, Linux, and all other Unix platforms. Registered users receive free updates. It was developed and is supported by Loehle Enterprises, 1258 Windemere Avenue, Naperville, IL 60564. The phone number is 630/579-1190; fax: 630/579-1195; email: craigloehl@aol.com.

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