Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem | Zendy

Wenli Liu | Zendy; Xiaoni Chi | Zendy; Qili Yang | Zendy; Ranran Cui | Zendy

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Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem

Author(s) -

Wenli Liu,

Xiaoni Chi,

Qili Yang,

Ranran Cui

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/6674520

Subject(s) - smoothing , mathematics , subgradient method , jacobian matrix and determinant , complementarity (molecular biology) , function (biology) , mathematical optimization , mixed complementarity problem , consistency (knowledge bases) , discrete mathematics , statistics , physics , nonlinear system , quantum mechanics , evolutionary biology , biology , genetics

In this paper, a weighted second-order cone (SOC) complementarity function and its smoothing function are presented. Then, we derive the computable formula for the Jacobian of the smoothing function and show its Jacobian consistency. Also, we estimate the distance between the subgradient of the weighted SOC complementarity function and the gradient of its smoothing function. These results will be critical to achieve the rapid convergence of smoothing methods for weighted SOC complementarity problems.

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