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＜電子ブック＞
Multilevel Optimization: Algorithms and Applications / edited by A. Migdalas, Panos M. Pardalos, Peter Värbrand
(Nonconvex Optimization and Its Applications ; 20)

版	1st ed. 1998.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1998
本文言語	英語
大きさ	XXII, 386 p : online resource
著者標目	Migdalas, A editor Pardalos, Panos M editor Värbrand, Peter editor SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Algorithms LCSH:Mathematical models LCSH:Computer science FREE:Optimization FREE:Algorithms FREE:Mathematical Modeling and Industrial Mathematics FREE:Theory of Computation
一般注記	1 Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions -- 1 Introduction -- 2 Literature Review -- 3 Model Analysis -- 4 Necessary Optimality Conditions of the DAP -- 5 Conclusions -- 2 Determining Tax Credits for Converting Nonfood Crops to Biofuels: An Application of Bilevel Programming -- 1 Introduction -- 2 Mathematical Model -- 3 Description of Algorithms -- 4 Computational Results -- 5 Discussion -- 3 Multilevel Optimization Methods in Mechanics -- 1 Introduction -- 2 Presentation of the Multilevel Decomposition Methods -- 3 Large Cable Structures -- 4 Large Elastoplastic Structures -- 5 Validation and Improvements of Simplified Models -- 6 Extension to other Problems. Decomposition Algorithms for Nonconvex Minimization Problems -- 7 A Multilevel Method for the Approximation of a Nonconvex Minimum Problem by Convex ones -- 8 Multilevel Decomposition into two Convex Problems -- 9 Structures with Fractal Interfaces -- 4 Optimal Structural Design in Nonsmooth Mechanics -- 1 Introduction -- 2 Parametric Nonsmooth Structural Analysis Problems -- 3 Optimal Design Problems -- 4 Mathematical Analysis and Algorithms -- 5 Discussion -- References -- 5 Optimizing the Operations of an Aluminium Smelter Using Non-Linear Bi-Level Programming -- 1 Introduction -- 2 The Mathematical Model of the Aluminium Smelter -- 3 The Solution Algorithm -- 4 The Mathematical Model Representing the Multi-period Operations of the Aluminium Smelter -- 5 Concluding Remarks -- References -- 6 Complexity Issues in Bilevel Linear Programming -- 1 Introduction -- 2 Difficulty in Approximation -- 3 A Special Case Solvable in Polynomial Time -- 4 Regret Ratio in Decision Analysis -- 5 Future Directions -- References -- 7 The Computational Complexity of Multi-Level Bottleneck Programming Problems -- 1 Introduction -- 2 Problem Statement and Previous Complexity Results -- 3 Hardness Proof for Multi-Level Bottleneck Programs -- 4 Hardness Proof for Multi-Level Linear Programs -- 5 The Complexity of Bi-Level Programs -- 6 Discussion -- References -- 8 On the Linear Maxmin and Related Programming Problems -- 1 Introduction -- 2 Reformulations -- 3 Tools for Resolution -- 4 Solving the Linear Maxmin Problem -- 9 Piecewise Sequential Quadratic Programming for Mathematical Programs with Nonlinear Complementarity Constraints -- 1 Introduction -- 2 Application to Optimal Design of Mechanical Structures -- 3 The Piecewise Smooth Approach to NCP-MP -- 4 The PSQP Method for NCP-MPEC -- 5 Computational Testing of PSQP -- References -- 10 A New Branch and Bound Method for Bilevel Linear Programs -- 1 Introduction -- 2 The Equivalent Reverse Convex Program -- 3 Solution Method -- 4 Implementation Issues -- 5 Illustrative Example -- 11 A Penalty Method for Linear Bilevel Programming Problems -- 1 Introduction -- 2 Linear Bilevel Programming Problem -- 3 The Method -- 4 Globalization of the Solution -- 5 Numerical Examples -- 6 Concluding Remarks -- 12 An Implicit Function Approach to Bilevel Programming Problems -- 1 Introduction -- 2 Lipschitz Continuity of Optimal Solutions -- 3 Application of the Bundle Method -- 4 Non-uniquely Solvable Lower Level Problems -- 5 Nonconvex Lower Level Problems and Coupling Constraints in the Upper Level Problem -- 13 Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming -- 1 Introduction -- 2 Optimization over the Efficient Set -- 3 Bilevel Linear Programming -- 4 Basic Properties of (FMRP) -- 5 Different D.C. Approaches to (FMRP) -- 14 Existence of Solutions to Generalized Bilevel Programming Problem -- 1 Introduction -- 2 Notations and Preliminaries -- 3 Parametric Implicit Variational Problem -- 4 Existence Results for Generalized Bilevel Problems -- 5 Final Remarks -- 15 Application of Topological Degree Theory to Complementarity Problems -- 1 Problem Specification and Topological Degree Theory -- 2 General Complementarity Problem -- 3 Sufficient Conditions for Solution Existence -- 4 Standard Complementarity Problem -- 5 Implicit Complementarity Problem -- 6 General Order Complementarity Problem -- References -- 16 Optimality and Duality in Parametric Convex Lexicographic Programming -- 1 Introduction -- 2 Orientation -- 3 Continuity -- 4 Global Optimality -- 5 Local Optimality -- 6 Duality -- 7 Bilevel Zermelo’s Problems 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) HTTP:URL=https://doi.org/10.1007/978-1-4613-0307-7

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