Boris S. Mordukhovich

Second-Order Variational Analysis in Optimization, Variational Stability, and Control (eBook, PDF)

Theory, Algorithms, Applications

• Format: PDF

Produktbeschreibung

first monograph entirely devoted to the rapidly developing area of second-order variational analysis and its applications to optimization, equilibria, stability, control, mechanics, and social-economic modeling.

includes recent results

contains a substantial number of exercises at various levels of difficulties with solution hints for more challenging ones

formulate open questions and conjectures together with extended commentaries and a large reference list at end of each chapter

comprehensive, systematically developed and entirely self-contained

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 789
• Erscheinungstermin: 21. Mai 2024
• Englisch
• ISBN-13: 9783031534768
• Artikelnr.: 70736512

Autorenporträt

Boris S. Mordukhovich is Distinguished Professor of Mathematics at Wayne State University. He has more than 500 publications including several monographs. Among his best known achievements are the introduction and development of powerful constructions of generalized differentiation and their applications to broad classes of problems in variational analysis, optimization, equilibrium, control, economics, engineering, and other fields. Mordukhovich is a SIAM Fellow, an AMS Fellow, and a recipient of many international awards and honors including Doctor Honoris Causa degrees from six universities over the world. He is a Highly Cited Researcher in Mathematics. His research has been supported by continued grants from the National Science Foundations and the Air Force Office of Scientific Research.

Inhaltsangabe

Preface.- 1. Basic Concepts of Second-Order Analysis.- 2. Second-Order Subdifferential Calculus.- 3. Computing Second-Order Subdifferentials.- 4. Computing Primal-Dual Second-Order Objects.- 5. Tilt Stability in Optimization.- 6. Full Stability in Optimization.- 7. Full Stability for Parametric Variational Systems.- 8. Critical Multipliers in Variational Systems.- 9. Newton-Type Methods for Tilt-Stable Minimizers.- 10. Sweeping Process Over Controlled Polyhedra.- 11. Sweeping Process with Controlled Perturbations.- 12. Sweeping Process Under Prox-Regularity.- 13. Applications to Controlled Crowd Motion Models.- References.- List of Statements.- List of Figures.- Glossary of Notation.- Subject Index.

Rezensionen

This book is a valuable resource to a wide range of readers including researchers in the areas of nonlinear, variational, and convex analysis, optimization and systems control, as well as graduate students. (Ilya A. Shvartsman, Mathematical Reviews, June, 2025)

This self-contained book, authored by a well-known expert in non-smooth analysis and optimization, is the first comprehensive work on second-order variational analysis, including both numerical algorithms and practical applications. Each chapter includes historical context, key definitions, theorems, and examples/exercises for readers to complete. This structure makes the book a useful resource for both lecturers and students and offers inspiration for PhD students. the book is a valuable resource that can be recommended to scientific researchers, students . (Wieslaw Kotarski, zbMATH 1551.49001, 2025)

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