ISBN:
9783031255649
Language:
English
Pages:
1 online resource (401 pages)
Edition:
1st ed.
Series Statement:
Complex Networks and Dynamic Systems Series v.5
Parallel Title:
Erscheint auch als
DDC:
629.04
Abstract:
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Introduction -- 1.2 Some DTA and DUE Literature -- 1.3 Vocabulary of DUE Modeling -- 1.4 Alternative Formulations of DUE -- 1.5 The Structure of DUE Models -- 1.6 Dynamic Network Loading Models -- 1.6.1 Vickrey's Model of a Traffic Bottleneck and Its Extension -- 1.6.2 Network Loading Based on Link Dynamics -- 1.6.3 Network Loading as a LWR-Based PDAE System -- 1.6.3.1 The Perakis-Kachani DNL Models -- 1.6.3.2 The Han-Friesz Within-Link Dynamicsfor DNL -- 1.6.4 Network Loading Based on the CTM -- 1.6.5 Network Loading Based on the Variational Approach -- 1.6.6 LWR Network Loading Based on Closed-Form Operators -- 1.6.7 Dynamic User Equilibrium in Continuous Time -- 1.6.8 Dynamic User Equilibrium in Discrete Time -- 1.7 Other Considerations in Classifying DUE Models -- 1.8 Unresolved/Partially Resolved Fundamental Challenges -- References and Suggested Reading -- 2 Mathematical Preliminaries -- 2.1 Selected Topics in Functional Analysis -- 2.1.1 Hilbert Spaces -- 2.1.2 Topological Vector Spaces -- 2.1.3 Compactness -- 2.1.4 The Contraction Mapping Theorem -- 2.2 Nonlinear Programming -- 2.2.1 Nonlinear Program Defined -- 2.2.2 The Fritz John Conditions -- 2.2.3 The Kuhn-Tucker Conditions -- 2.2.4 Kuhn-Tucker Conditions Sufficient -- 2.2.5 Kuhn-Tucker Conditions for Variational Inequalities -- 2.3 Calculus of Variations -- 2.3.1 The Space C1[t0,tf] -- 2.3.2 The Concept of a Variation -- 2.4 Optimal Control -- 2.4.1 The State Operator -- 2.4.2 Necessary Conditions for Continuous-TimeOptimal Control -- 2.4.3 Sufficiency in Optimal Control -- 2.4.3.1 The Mangasarian Theorem -- 2.4.3.2 The Arrow Theorem -- 2.5 Differential Variational Inequalities -- 2.5.1 Problem Definition -- 2.5.2 Regularity Conditions for DIV -- 2.5.3 Necessary Conditions -- 2.6 Nash Games and Differential Nash Games.
Note:
Description based on publisher supplied metadata and other sources
