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

This paper describes the theory and a new algorithm for computing the parameterized solution to a family of minmax problems (MMP): min max Ji (u,z), z??Z. u??U i??I It is shown that MMP may be solved indirectly by looking for the saddle point of ??I??I ciJi(u,z). This result enables an important type of MMP to be reduced by analytic manipulation into a family of inequality constrained programming problems. Over partitioning subsets of Z, the solution ?? to this latter family of problems may be found by solving appropriate equality constrained problems. Two important new results are proved: one concerns the continuity of the solution ?? over line segments in Z and the other concerns linearity of the interset boundaries separating the partitioning subsets of Z. 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.