Hierarchical Optimization and Mathematical Physics

2000. Auflage 2000
ISBN: 978-0-7923-6175-6
Verlag: Springer

Buch, Englisch, Band 37, 310 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1390 g

Reihe: Applied Optimization

This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problern with macrovariables, whose number is less than the number of initial variables. This problern is often very simple. On the lower level, we have the usual optimal control problems of math­ ematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems ofless dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problern and converge to its optimal solutionunder certain assumptions ( e.g., under strict convexity of the input functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assem­ bles the final production from the components produced by the subsystems.

Zielgruppe

Research

Autoren/Hrsg.

Tsurkov, Vladimir

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

Preface. 1. The Main Model and Constructions of the Decomposition Method. 2. Generalization of the Decomposition Approach to Mathematical Programming and Classical Calculus of Variations. 3. Hierarchical Systems of Mathematical Physics. 4. Effectiveness of Decomposition. 5. Appendix. The Main Approaches in Hierarchical Optimization. Index.