The Interactive command displays a Maplet application that provides a graphical user interface to the solver routines in the Optimization and GlobalOptimization packages. You can select one of the methods shown in the interface to obtain a minimum (or maximum) of a function under the given constraints.

When you click the Solve button, the problem (the objective function, constraints, bounds, and options) is solved using the indicated method, and the solution is provided in the Solution area of the Maplet application.

When a solution is obtained, clicking the Plot button displays a plot of the objective function in the region of the solution or, if the problem is bounded, a plot of the objective function over the search region.

The plot is obtained with respect to either one or two of the problem variables, corresponding to a 2-D or 3-D plot respectively, fixing all other problem variables to their values at the computed optimum.

The constraints can be plotted as lines on the surface of the objective function or as vertical planes intersecting the objective function.

If the first calling sequence is used, the objective function and constraints can be entered in the Maplet interface. If the second calling sequence is used, the parameter obj is an algebraic expression representing the function to be minimized or maximized.  If provided, the parameter constr must be a set of relations (of type <= or =) involving the problem variables. Bounds, of the form variable = lower .. upper, can also be included in the set.

The Maplet application uses the algebraic form of input as described in the Optimization/AlgebraicForm and GlobalOptimization/AlgebraicForm help pages.  Alternative forms of input, described in Optimization/InputForms and GlobalOptimization/InputForms, are recognized by the Optimization and GlobalOptimization package routines, but are not available in the Maplet application.

Most options for the Optimization and GlobalOptimization routines can be set or changed in the Maplet application. These options are described in detail in the Optimization/Options and GlobalOptimization/Options help pages.

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

$\mathrm{Interactive}\left(x\&plus;y\&comma;\left\{1\le x\&plus;y\&comma;x\&equals;0..1\&comma;y\&equals;0..1\right\}\right)$