The objective function must be an algebraic expression in the problem variables, for example, ${\ⅇ}^{\tan \left(x\right)}$ 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.

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

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.

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}.

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.

$\mathrm{with}\left(\mathrm{GlobalOptimization}\right)\&colon;$

$\mathrm{GlobalSolve}\left(y^2-10x-5y\&comma;\left\{-2x^4-y=-2\right\}\&comma;x=0..3\&comma;y=0..3\right)$

$\left[\mathrm{-12.5142127851561753}\&comma;\left[x=0.788704583952784\&comma;y=1.22609535114607\right]\right]$

$\mathrm{GlobalSolve}\left({\left(x-1\right)}^2+{\left(y-2\right)}^2+{\left(z-3\right)}^2\&comma;\left\{x^2+y^2+z^2=0.5\right\}\&comma;x=0..1\&comma;y=0..1\&comma;z=0..1\right)$

$\left[9.20849737787081501\&comma;\left[x=0.188982236070483\&comma;y=0.377964472954812\&comma;z=0.566946709694829\right]\right]$