Multilevel Optimization: Algorithms and Applications

✍ Scribed by Yang Chen, Michael Florian (auth.), Athanasios Migdalas, Panos M. Pardalos, Peter Värbrand (eds.)

• Publisher: Springer US
• Year: 1998
• Tongue: English
• Leaves: 402
• Series: Nonconvex Optimization and Its Applications 20
• Edition: 1
• Category: Library

✦ Synopsis

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 uncer­ tain 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 hierar­ chies is to focus on one level and include other levels' behaviors as assumptions. Multilevel programming is the research area that focuses on the whole hierar­ chy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of opti­ mization 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).

✦ Table of Contents

Front Matter....Pages i-xxii
Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions....Pages 1-22
Determining Tax Credits for Converting Nonfood Crops to Biofuels: An Application of Bilevel Programming....Pages 23-50
Multilevel Optimization Methods in Mechanics....Pages 51-90
Optimal Structural Design in Nonsmooth Mechanics....Pages 91-115
Optimizing the Operations of an Aluminium Smelter Using Non-Linear Bi-Level Programming....Pages 117-148
Complexity Issues in Bilevel Linear Programming....Pages 149-164
The Computational Complexity of Multi-Level Bottleneck Programming Problems....Pages 165-179
On the Linear Maxmin and Related Programming Problems....Pages 181-208
Piecewise Sequential Quadratic Programming for Mathematical Programs with Nonlinear Complementarity Constraints....Pages 209-229
A New Branch and Bound Method for Bilevel Linear Programs....Pages 231-249
A Penalty Method for Linear Bilevel Programming Problems....Pages 251-271
An Implicit Function Approach to Bilevel Programming Problems....Pages 273-294
Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming....Pages 295-314
Existence of Solutions to Generalized Bilevel Programming Problem....Pages 315-332
Application of Topological Degree Theory to Complementarity Problems....Pages 333-358
Optimality and Duality in Parametric Convex Lexicographic Programming....Pages 359-379
Back Matter....Pages 381-386

✦ Subjects

Optimization; Algorithms; Mathematical Modeling and Industrial Mathematics; Theory of Computation