Linear complementarity problems on extended second order cones

Sandor Nemeth; Lianghai Xiao

doi:10.1007/s10957-018-1220-x

Linear complementarity problems on extended second order cones

Sandor Nemeth, Lianghai Xiao

Mathematics

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Abstract

In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg–Marquardt algorithm. Finally, we present some numerical examples.

Original language	English
Pages (from-to)	269-288
Journal	Journal of Optimization Theory and Applications
Volume	176
Issue number	2
Early online date	17 Jan 2018
DOIs	https://doi.org/10.1007/s10957-018-1220-x
Publication status	Published - 25 Feb 2018

Keywords

complementarity problem
extended second order cone
conic optimization

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title = "Linear complementarity problems on extended second order cones",

abstract = "In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg–Marquardt algorithm. Finally, we present some numerical examples.",

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AU - Xiao, Lianghai

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N2 - In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg–Marquardt algorithm. Finally, we present some numerical examples.

AB - In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg–Marquardt algorithm. Finally, we present some numerical examples.

KW - complementarity problem

KW - extended second order cone

KW - conic optimization

U2 - 10.1007/s10957-018-1220-x

DO - 10.1007/s10957-018-1220-x

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JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

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Linear complementarity problems on extended second order cones

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