A piecewise-closed form algorithm for a family of minmax and vector criteria problems

This short paper describes the theory and a new algorithm for computing the parameterized solution to a family of minmax problems . The fact that MMP may be solved indirectly by looking for the saddle point of enables an important special class of MMP to be reduced by analytic manipulation into a family of inequality constrained programming problems. Over partitioning subsets of , the solution ω to this latter family of problems may be found by solving appropriate equality constrained problems. Two important new results are established: one concerns the continuity of the solution ω in and the other concerns linearity of the interset boundaries separating the partitioning subsets of . These results are incorporated into the new algorithm which proves to be excellent for obtaining the parameterized solution of certain types of families of minmax problems.