On the Lorentz Cone Complementarity Problems in Infinite-Dimensional Real Hilbert Space

Miao, Xin He; Chen, Jein Shan

doi:10.1080/01630563.2011.563893

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2015

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“…There has been extensively research on SOC [5,6] , especially on some properties of solutions of the second-order cone complementarity problem(SOCCP). There are many results on the properties of solutions for complementarity problems in both finite-dimensional and infinite-dimensional settings [1,4,6,[7][8][9][10][11] . In the finitedimensional space, Gowda and Sznajder [12] studied the conditions which guarantees that the linear transformation T has the GUS-property.…”

Section:  mentioning

confidence: 99%

Feasibility and structural feature on monotone second-order cone linear complementarity problems in Hilbert space

Miao

Guo

2015

Trans. Tianjin Univ.

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Abstract：Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element H  q. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.

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Section:  mentioning

confidence: 99%