SOC functions

Jein Shan Chen*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter


During the past two decades, there have been active research for second-order cone programs (SOCPs) and second-order cone complementarity problems (SOCCPs). Various methods had been proposed which include the interior-point methods [1, 102, 109, 123, 146], the smoothing Newton methods [51, 63, 71], the semismooth Newton methods [86, 120], and the merit function methods [43, 48]. All of these methods are proposed by using some SOC complementarity function or merit function to reformulate the KKT optimality conditions as a nonsmooth (or smoothing) system of equations or an unconstrained minimization problem. In fact, such SOC complementarity functions or merit functions are closely connected to so-called SOC functions. In other words, studying SOC functions is crucial to dealing with SOCP and SOCCP, which is the main target of this chapter.

Original languageEnglish
Title of host publicationSpringer Optimization and Its Applications
PublisherSpringer International Publishing
Number of pages37
Publication statusPublished - 2019

Publication series

NameSpringer Optimization and Its Applications
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

ASJC Scopus subject areas

  • Control and Optimization


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