SOC functions

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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
Pages1-37
Number of pages37
DOIs
Publication statusPublished - 2019 Jan 1

Publication series

NameSpringer Optimization and Its Applications
Volume143
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

Fingerprint

Second-order Cone
Merit Function
Complementarity Problem
Complementarity
KKT Conditions
Smoothing Newton Method
Semismooth Newton Method
Unconstrained Minimization
Interior Point Method
Optimality Conditions
Minimization Problem
System of equations
Smoothing
Target

ASJC Scopus subject areas

  • Control and Optimization

Cite this

Chen, J. S. (2019). SOC functions. In Springer Optimization and Its Applications (pp. 1-37). (Springer Optimization and Its Applications; Vol. 143). Springer International Publishing. https://doi.org/10.1007/978-981-13-4077-2_1

SOC functions. / Chen, Jein Shan.

Springer Optimization and Its Applications. Springer International Publishing, 2019. p. 1-37 (Springer Optimization and Its Applications; Vol. 143).

Research output: Chapter in Book/Report/Conference proceedingChapter

Chen, JS 2019, SOC functions. in Springer Optimization and Its Applications. Springer Optimization and Its Applications, vol. 143, Springer International Publishing, pp. 1-37. https://doi.org/10.1007/978-981-13-4077-2_1
Chen JS. SOC functions. In Springer Optimization and Its Applications. Springer International Publishing. 2019. p. 1-37. (Springer Optimization and Its Applications). https://doi.org/10.1007/978-981-13-4077-2_1
Chen, Jein Shan. / SOC functions. Springer Optimization and Its Applications. Springer International Publishing, 2019. pp. 1-37 (Springer Optimization and Its Applications).
@inbook{10738321a20749e29057eb25c88a3cc2,
title = "SOC functions",
abstract = "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.",
author = "Chen, {Jein Shan}",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-981-13-4077-2_1",
language = "English",
series = "Springer Optimization and Its Applications",
publisher = "Springer International Publishing",
pages = "1--37",
booktitle = "Springer Optimization and Its Applications",

}

TY - CHAP

T1 - SOC functions

AU - Chen, Jein Shan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062676426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062676426&partnerID=8YFLogxK

U2 - 10.1007/978-981-13-4077-2_1

DO - 10.1007/978-981-13-4077-2_1

M3 - Chapter

AN - SCOPUS:85062676426

T3 - Springer Optimization and Its Applications

SP - 1

EP - 37

BT - Springer Optimization and Its Applications

PB - Springer International Publishing

ER -