Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem. (23rd January 2021)

• Record Type: Journal Article
• Authors: Liu, Wenli; Chi, Xiaoni; Yang, Qili; Cui, Ranran
• Other Names: Wang Guoqiang Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-01-23
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/6674520
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.