The Interval Global Solver included free with the Premium Solver Platform uses interval methods to find globally optimal solutions for constrained nonlinear optimization problems, all real solutions for systems of nonlinear equations, or "inner solutions" for systems of inequalities.
Using the unique ability of the Polymorphic Spreadsheet Interpreter in Premium Solver Platform to compute interval values and interval gradients for Excel formulas, it overcomes the limitations of classical nonlinear methods -- which can find only locally optimal solutions -- and finds the "true" globally optimal solution (subject only to limitations due to roundoff error).
The Premium Solver Platform's Interval Global Solver is a truly pioneering Solver engine. It uses the Moore-Skelboe Interval Branch and Bound algorithm to systematically and efficiently search the region enclosed by the bounds on the variables for all locally optimal solutions, or all real solutions of a system of equations. It employs a variety of methods to tighten bounds on regions or reduce the size of "boxes," including the mean value form and the Interval Newton method with the Krawczyk operator, the linear enclosure form and the Simplex method for linear enclosures of constraints, and interval constraint propagation using both hull consistency and box consistency methods.
New Solutions Report
The Premium Solver Platform also includes a new Solutions Report for problems solved with the Interval Global Solver. (Click on the worksheet to see it full size.)
For a system of nonlinear equations, the Answer Report shows only a single solution, but the Solutions Report shows you all real solutions. For a system of inequalities, the Answer Report again shows you only a single feasible point, but the Solutions Report shows you an "inner solution" -- a region or set of points where all of the constraints are satisfied.