TY - JOUR

T1 - The Hölder continuity of vector-valued function associated with second-order cone

AU - Chang, Yu-Lin

AU - Chen, Jein-Shan

PY - 2012/1/1

Y1 - 2012/1/1

N2 - Let Kn be the Lorentz/second-order cone in IRn. For any function f from IR to IR, one can define a corresponding vector-valued function fsoc (x) on IRn by applying f to the spectral values of the spectral decomposition of x ∈ IRn with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng in [5] that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as semismoothness. In this note, we further show that the Holder continuity of this vector-valued function is also inherited from f. Such property will be useful in designing solution methods for second-order cone programming and second-order cone complementarity problem.

AB - Let Kn be the Lorentz/second-order cone in IRn. For any function f from IR to IR, one can define a corresponding vector-valued function fsoc (x) on IRn by applying f to the spectral values of the spectral decomposition of x ∈ IRn with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng in [5] that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as semismoothness. In this note, we further show that the Holder continuity of this vector-valued function is also inherited from f. Such property will be useful in designing solution methods for second-order cone programming and second-order cone complementarity problem.

KW - Hölder continuity

KW - Second-order cone

UR - http://www.scopus.com/inward/record.url?scp=84874888057&partnerID=8YFLogxK

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M3 - Article

AN - SCOPUS:84874888057

VL - 8

SP - 135

EP - 141

JO - Pacific Journal of Optimization

JF - Pacific Journal of Optimization

SN - 1348-9151

IS - 1

ER -