A set of candidate global optima is identified, one of which is a global solution for making a mask for printing a lithographic pattern. A solution space is formed from dominant joint eigenvectors that is constrained for bright and dark areas of the printed pattern. The solution space is mapped to identify regions each containing at most one local minimum intensity. For each selected region, stepped intensity contours are generated for intensity of the dark areas and stepped constraint surfaces are generated for a target exposure dose at an individual test point. An individual test point is stepped toward a lowest intensity contour along the stepped constraint surfaces of each selected region. Further lowering of the intensities of these points is also detailed, where possible in adjacent regions, to yield final test points. The set of candidate global optima is the final test points at their respective lowest intensity contour of the respective selected regions.