Sigma-piecewise functions and problems of disjunctive programming

Some special statements of mathematical programming problems are considered. The feasible domain is defined by disjunction of constraints, unlike traditional formulations, where the domain is determined as the intersection of sets. A problem of piecewise linear programming is an important particular case. The notion of disjunctive Lagrangian is introduced. Theorems of Kuhn-Tucker type, duality theorems, theorems on exact penalty functions, etc. cire formulated.