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About the problem of disjunctive programming. (English) Zbl 1006.90063

The author describes an original conceptual approach to the problems of disjunctive programming where the feasible set is a union of infinitely many components described by inequalities. The concept of disjunctive Lagrangian function is introduced and sufficient conditions for optimality are formulated in terms of its saddle points. Furthermore, a duality framework for disjunctive programming is constructed and relations between primal and dual problems are investigated. Finally, an exact penalty function method for disjunctive programming is formulated and its theoretical properties are analyzed.

MSC:

90C26 Nonconvex programming, global optimization
90C46 Optimality conditions and duality in mathematical programming
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