Migdalas A., Pardalos P.M., Värbrand P. (eds.) Multilevel Optimization. Algorithms and Applications

Kluwer, 1998. — 261 p.Researchers working with nonlinear programming often claim "the word is non-linear" indicating that real applications require nonlinear modeling. The same is true for other areas such as multi-objective programming (there are always several goals in a real application), stochastic programming (all data is uncertain and therefore stochastic models should be used), and so forth. In this spirit we claim: The word is multilevel. In many decision processes there is a hierarchy of decision makers, and decisions are made at different levels in this hierarchy. One way to handle such hierarchies is to focus on one level and include other levels' behaviors as assumptions. Multilevel programming is the research area that focuses on the whole hierarchy structure. In terms of modeling, 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. If only two levels are considered, we have one leader (associated with the upper level) and one follower (associated with the lower level).Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions
Determining Tax Credits for Converting Nonfood Crops to Biofuels: An Application of Bilevel Programming
Multilevel Optimization Methods in Mechanics
Optimal Structural Design in Nonsmooth Mechanics
Optimizing the Operations of an Aluminium Smelter using Non-Linear Bi-Level Programming
Complexity Issues in Bilevel Linear Programming
The Computational Complexity of Multi-Level Bottleneck Programming Problems
On the Linear Maxmin and Related Programming Problems
Piecewise Sequential Quadratic Programming for Mathematical Programs with Nonlinear Complementarity Constraints
A New Branch and Bound Method for Bilevel Linear Programs
A Penalty Method for Linear Bilevel Programming Problems
An Implicit Function Approach to Bilevel Programming Problems
Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming
Existence of Solutions to Generalized Bilevel Programming Problem
Application of Topological Degree Theory to Complementarity Problems
Optimality and Duality in Parametric Convex Lexicographic Programming