SOC Functions and Their Applications

1. Auflage 2019
ISBN: 978-981-13-4076-5
Verlag: Springer Nature Singapore

Buch, Englisch, Band 143, 206 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 494 g

Reihe: Springer Optimization and Its Applications

This book covers all of the concepts required to tackle second-order cone programs (SOCPs), in order to provide the reader a complete picture of SOC functions and their applications. SOCPs have attracted considerable attention, due to their wide range of applications in engineering, data science, and finance. To deal with this special group of optimization problems involving second-order cones (SOCs), we most often need to employ the following crucial concepts: (i) spectral decomposition associated with SOCs, (ii) analysis of SOC functions, and (iii) SOC-convexity and -monotonicity.

 Moreover, we can roughly classify the related algorithms into two categories. One category includes traditional algorithms that do not use complementarity functions. Here, SOC-convexity and SOC-monotonicity play a key role. In contrast, complementarity functions are employed for the other category. In this context, complementarity functions are closely related to SOC functions; consequently, the analysis of SOC functions can help with these algorithms.

Zielgruppe

Research

Autoren/Hrsg.

Chen, Jein-Shan

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung

Inhaltsverzeichnis

SOC Functions.- SOC-convexity and SOC-Monotonity.- Algorithmic Applications.- SOC Means and SOC Inequalities.- Possible Extensions.