Nonconvex Optimization and Its Applications Multilevel Optimization: Algorithms

Researchers working with nonlinear programming often claim "the word is non­ linear" indicating that real applications require nonlinear modeling. If only two levels are considered, we have one leader (associated with the upper level) and one follower (associated with the lower level). In many decision processes there is an hierarchy of decision-makers and decisions are taken at different levels in this hierarchy. Multilevel programming focuses on the whole hierarchy structure. In terms of modelling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of optimization problems which must be solved in a predetermined sequence. The field of multilevel optimization has become a well-known and important research field. Hierarchical structures can be found in scientific disciplines such as environment, ecology, biology, chemical engineering, mechanics, classification theory, databases, network design, transportation, game theory and economics. Moreover, new applications are constantly being introduced. This has stimulated the development of new theory and efficient algorithms. This volume contains 16 chapters written by various researchers and presents a cohesive overview of developments and applications in the emerging field of optimization. This text is intended for researchers whose work involves the application of mathematical programming and optimization to hierarchical structures.