The monotone extended second-order cone and mixed complementarity problems

Yingchao Gao, Sandor Nemeth, Roman Sznajder

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Abstract

In this paper, we study a new generalization of the Lorentz cone Ln+, called the monotone extended second-order cone (MESOC). We investigate basic properties of MESOC including computation of its Lyapunov rank and proving its reducibility. Moreover, we show that in an ambient space, a cylinder is an isotonic projection set with respect to MESOC. We also examine a nonlinear complementarity problem on a cylinder, which is equivalent to a suitable mixed complementarity problem, and provide a computational example illustrating applicability of MESOC.
Original languageEnglish
Pages (from-to)381-407
Number of pages27
JournalJournal of Optimization Theory and Applications
Volume193
Issue number1-3
Early online date29 Nov 2021
DOIs
Publication statusPublished - Jun 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).

Keywords

  • Complementarity problems
  • Lyapunov rank
  • Monotone extended second-order cone

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

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