On general decomposition schemes in mathematical programming

A general decomposition technique in ordered structures is described which can be applied to algebraic mathematical programs and which reduces to Benders' and Dantzig-Wolfe decomposition in the classical linear case. This approach enables applying decomposition to problems involving bottleneck, multi criteria and fuzzy functions with real or integer variables. The decomposition procedure is based on general duality theory. Moreover, an extension of the so-called cross decomposition procedure is discussed.