Overview of the GlobalOptimization Package - Maple Programming Help

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Overview of the GlobalOptimization Package

 Calling Sequence GlobalOptimization[command](arguments) command(arguments)

Description

 • The Global Optimization Toolbox, powered by Optimus® technology from Noesis Solutions, is implemented as the GlobalOptimization package, which numerically computes global solutions to nonlinear programming (NLP) problems over a bounded region.  An NLP problem is the minimization or maximization of an objective function, possibly subject to constraints.
 • The GlobalOptimization package contains a command for solving optimization problems, which can be specified in various forms. For information on the input forms, see the GlobalOptimization/InputForms help page. Additionally, the package offers an interactive Maplet interface that provides an easy-to-use facility for entering and solving an optimization problem, as well as plotting both the problem and its solution.
 • Using the many options, you can control the algorithms used by the global solver. For information on these options, see the GlobalOptimization/Options help page.
 • The global solver in the GlobalOptimization package calls external code that uses hardware floats, but the objective function and the constraints can be evaluated in Maple with higher precision.   For more information on the global solver, the algorithms, the floating-point computation environment, and ways to achieve best performance with the solver, see the GlobalOptimization/Computation help page.
 • For more information and examples on the toolbox, see Introduction to the Global Optimization Toolbox and Applications of the Global Optimization Toolbox.

Accessing Package Commands

 • Each command in the GlobalOptimization package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 Because the underlying implementation of the package is a module, it is possible to use the form GlobalOptimization:-command to access a command from the package. For more information, see Module Members.

List of Package Commands

 • The following is a list of available commands.

 To display the help page for a particular command, see Getting Help with a Command in a Package.
 • The GlobalSolve help page describes the most commonly used forms of input.  Use with the more advanced Matrix form of input is described in the GlobalOptimization[GlobalSolveMatrixForm] help page.

Notes

 • To see additional information on the progress of the solver during the solution of an optimization problem, set infolevel[GlobalOptimization] to a positive integer.  More information is printed at higher infolevel settings.

Examples

 > $\mathrm{with}\left(\mathrm{GlobalOptimization}\right):$

Find the global solution to the minimization problem $\mathrm{ln}\left(x\right)\mathrm{sin}\left(x\right)$ in the range $\left[1..20\right]$.

 > $\mathrm{GlobalSolve}\left(\mathrm{ln}\left(x\right)\mathrm{sin}\left(x\right),x=1..20\right)$
 $\left[{-2.85006479973796}{,}\left[{x}{=}{17.2990352355127}\right]\right]$ (1)

Find the global solution to a constrained minimization problem.

 > $\mathrm{GlobalSolve}\left({x}^{6}-5{x}^{3}-20{x}^{2}-5,\left\{5{x}^{2}+20x+18\le 0\right\},x=-3..3\right)$
 $\left[{-23.0747312455205424}{,}\left[{x}{=}{-1.36754446796582}\right]\right]$ (2)