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Let K be a closed convex set in E superscript (m + 1) and L = (P = (P sub 0, ..., P sub m): P sub 1 = P sub 2 = ...P sub m = 0). Then for the simple problem: Minimize P sub 0 Subject to P = (P sub 0, P sub 1, ..., P sub m) epsilon the intersection of K and L, we prove a duality theorem and the convergence of a solution algorithm modeled on the duality theorem and the simplex method of linear programming respectively. Specialization of this general model to linear programming, convex programming, generalized programming, control theory, and the decomposition approach to mathematical programming yield the appropriate duality theorems and solution algorithms in each case.