Equivalence among optimization problems on matrix sets

AbstractTreatment of optimization problems on matrix sets is a general framework for the study of some large classes of discrete programming problems, for the investigation of connections between different classes of such problems. An appropriate formalism is introduced. It gives a possibility to include in this study bottle-neck problems and other combinatorial optimization problems over totally ordered commutative semigroups. Concepts of equivalency and of weak equivalency are defined and some general equivalency theorems are proved. The main problem under discussion is for which problems an equivalent problem over a finite ordered algebraic structure can be constructed