SOC Functions and Their Applications

  • Jein-Shan Chen

Part of the Springer Optimization and Its Applications book series (SOIA, volume 143)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jein-Shan Chen
    Pages 1-37
  3. Jein-Shan Chen
    Pages 39-99
  4. Jein-Shan Chen
    Pages 101-158
  5. Jein-Shan Chen
    Pages 159-188
  6. Jein-Shan Chen
    Pages 189-200
  7. Back Matter
    Pages 201-206

About this book


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.


second-order cone programs spectral decomposition SOC-convexity SOC-monotonicity SOC Functions

Authors and affiliations

  • Jein-Shan Chen
    • 1
  1. 1.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan

Bibliographic information

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