Topological Aspects of Nonsmooth Optimization

2012
ISBN: 978-1-4939-0069-5
Verlag: Springer

Buch, Englisch, 196 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 324 g

Reihe: Nonconvex Optimization and Its Applications

This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness.

Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory.

Zielgruppe

Research

Autoren/Hrsg.

Shikhman, Vladimir

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Preface. -Notation.- Introduction.-  Mathematical Programming Problems with Complementarity.- Constraints.-  General Semi-infinite Programming Problems.- Mathematical Programming Problems with Vanishing Constraints.- Bilevel Optimization.-  Impacts on Nonsmooth Analysis.- Appendix.- Bibliography.- References.- Index.