Nonlinear Programming and Variational Inequality Problems : A Unified Approach

Michael Patriksson

ISBN 10: 0792354559 / ISBN 13: 9780792354550

Editore: Springer US, 1998

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Zustand: Gut | Sprache: Englisch | Produktart: Bücher.

Codice articolo 3029187/203

Dati bibliografici

• Titolo: Nonlinear Programming and Variational Inequality Problems : A Unified Approach
• Editore: Springer US
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0792354559
• ISBN 13: 9780792354550
• Rilegatura: Rilegato
• Condizione: Gut
• Cataloghi dei venditori:
  • Bücher

Descrizione articolo

Riassunto

Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi­ mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal­ ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Contenuti

Preface. 1. Introduction. 2. Technical Preliminaries. 3. Instances of the Cost Approximation Algorithm. 4. Merit Functions for Variational Inequality Problems. 5. Convergence of the CA Algorithm for Nonlinear Programs. 6. Convergence of the CA Algorithm for Variational Inequality Problems. 7. Finite Identification of Active Constraints and of Solutions. 8. Parallel and Sequential Decomposition CA Algorithms. 9. A Column Generation/Simplicial Decomposition Algorithm. A. Definitions. References. Index.