The monotone extended second-order cone and mixed complementarity problems

Yingchao Gao; Sandor Nemeth; Roman Sznajder

doi:10.1007/s10957-021-01962-4

The monotone extended second-order cone and mixed complementarity problems

Yingchao Gao, Sandor Nemeth, Roman Sznajder

Mathematics

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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 language	English
Pages (from-to)	381-407
Number of pages	27
Journal	Journal of Optimization Theory and Applications
Volume	193
Issue number	1-3
Early online date	29 Nov 2021
DOIs	https://doi.org/10.1007/s10957-021-01962-4
Publication status	Published - 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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GaoY2021monotoneFinal published version, 405 KBLicence: Creative Commons: Attribution (CC BY)

Cite this

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AB - 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.

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The monotone extended second-order cone and mixed complementarity problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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