1. A method for outputting a set of candidate global optimum points for a mask used to make a lithographic printed pattern, the method comprising: defining a solution space formed from dominant joint eigenvectors for the printed pattern that is both constrained to be bright for bright areas of the printed pattern and that is constrained to be dark for dark areas of the printed pattern; mapping the solution space to identify regions, each region containing at most one local minimum intensity for a dark area; selecting at least some of the regions for test point analysis; for each of the selected regions, generating stepped intensity contours for intensity of the dark areas and stepped constraint surfaces for a target exposure dose at an individual bright point; within each selected region choosing a test point at the center of the selected region; within each selected region, progressively stepping the test point toward a lowest intensity contour along the stepped constraint surfaces to yield a final test point; outputting a set of candidate global optimum points that comprise the final test points at their respective lowest intensity contour of the respective selected region.