Cost-effective computational decision-making methods are considered. Provides the necessary information about binary relations, selection functions, and possible approaches to binary relation optimization. An overview of modern efficient linear and convex programming methods that can be used in computational schemes of selection algorithms is given. Different versions of a fairly universal model are presented - generalized mathematical programming (WMD), which fits many decision-making tasks. Design scheme of analysis and numerical solution of linear and convex WMD problems is developed and evaluated.