Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities

Minghua Li; Chunrong Chen; Shengjie Li

doi:10.3934/jimo.2019001

Article Contents

2020, Volume 16, Issue 3: 1261-1272. Doi: 10.3934/jimo.2019001

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Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities

1.
School of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan, Chongqing, 402160, China
2.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

^* Corresponding author: Minghua Li
^* Corresponding author: Minghua Li

Received: October 31, 2016

Revised: October 31, 2018

Early access: March 2019

Published: March 2020

The work was supported in part by the National Natural Science Foundation of China (Grant numbers: 11301418, 11301567, 11571055), the Natural Science Foundation of Chongqing Municipal Science and Technology Commission (Grant numbers: cstc2016jcyjA0141, cstc2016jcyjA0270, cstc2018jcyjAX0226), the Basic Science and Frontier Technology Research of Yongchuan (Grant number: Ycstc, 2018nb1401), the Fundamental Research Funds for the Central Universities (Grant Number: 106112017CDJZRPY0020), the Foundation for High-level Talents of Chongqing University of Art and Sciences (Grant numbers: R2016SC13, P2017SC01), the Chongqing Key Laboratory of Group and Graph Theories and Applications and the Key Laboratory of Complex Data Analysis and Artificial Intelligence of Chongqing Municipal Science and Technology Commission

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Abstract

In this paper, the Clarke generalized Jacobian of the generalized regularized gap function for a nonmonotone Ky Fan inequality is studied. Then, based on the Clarke generalized Jacobian, we derive a global error bound for the nonmonotone Ky Fan inequalities. Finally, an application is given to provide a descent method.

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Mathematics Subject Classification: Primary: 65K10, 90C31; Secondary: 90C33.

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