 Algebraic Form of Input for the GlobalOptimization Package - Maple Programming Help

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Algebraic Form of Input for the GlobalOptimization Package

 This help page describes the algebraic form of input for commands in the GlobalOptimization package.  For general information on the input forms accepted by the GlobalOptimization package commands, see the GlobalOptimization/InputForms help page.   For more information about options mentioned below, see the Optimization/Options help page.

Objective Function

 • The objective function must be an algebraic expression in the problem variables, for example, ${ⅇ}^{\mathrm{tan}\left(x\right)}$ and ${x}^{2}+{y}^{2}-3x+3y+3$.  The problem variables are the indeterminates in the objective function and, if provided, the constraints.  They can also be specified using the variables option.

Constraints

 • The constraints must be a set or list of relations.  Only relations of type <= and = are allowed.  An example is $\left\{w=1,2\le {y}^{2}+z,x\le 5\right\}$.

Bounds

 • Specify the bounds as a sequence of arguments of the form vname = vrange, where vname is the name of a problem variable and vrange is its range, for example, y=-1..2. There must be exactly one bound argument for each problem variable. The endpoints of each range must evaluate to finite numeric values.
 • Because finite bounds are required, the assume = nonnegative option, available in the Optimization package, is not accepted by GlobalOptimization commands.

Initial Values

 • Specify the initial values using the option initialpoint = p, where p is a set or list of equalities of the form varname=value. Each varname is one of the problem variables and value is the value to which it is initially set.  An example is initialpoint={x=-1.2, y=5.7}.

Solution

 • Maple returns the solution as a list containing the final minimum (or maximum) value and a point (the computed extremum).  The point is a list containing elements of the form $\mathrm{varname}=\mathrm{value}$, where varname is a problem variable and value is its value.

Examples

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

Solve a minimization problem in two variables, $x$ and $y$.

 > $\mathrm{GlobalSolve}\left({y}^{2}-10x-5y,\left\{-2{x}^{4}-y=-2\right\},x=0..3,y=0..3\right)$
 $\left[{-12.5142127851561753}{,}\left[{x}{=}{0.788704583952784}{,}{y}{=}{1.22609535114607}\right]\right]$ (1)

Solve a minimization problem in three variables, $x$, $y$, and $z$.

 > $\mathrm{GlobalSolve}\left({\left(x-1\right)}^{2}+{\left(y-2\right)}^{2}+{\left(z-3\right)}^{2},\left\{{x}^{2}+{y}^{2}+{z}^{2}=0.5\right\},x=0..1,y=0..1,z=0..1\right)$
 $\left[{9.20849737787081501}{,}\left[{x}{=}{0.188982236070483}{,}{y}{=}{0.377964472954812}{,}{z}{=}{0.566946709694829}\right]\right]$ (2)