Error Bounds of Regularized Gap Functions for Polynomial Variational Inequalities

被引：2

作者：

Van Dinh, Bui ^{[1
,2
]}

Pham, Tien-Son ^{[3
]}

机构：

[1] Le Quy Don Tech Univ, Dept Math, Hanoi, Vietnam

[2] VAST, Inst Math, Dept Optimizat & Control Theory, Hanoi, Vietnam

[3] Dalat Univ, Dept Math, 1 Phu Dong Thien Vuong, Da Lat, Vietnam

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2022年 / 192卷 / 01期

关键词：

Variational inequality; Regularized gap function; Error bound; Lojasiewicz inequality; Polynomial; OPTIMIZATION; NONSMOOTH; ALGORITHMS; STABILITY; SYSTEMS; SETS;

D O I：

10.1007/s10957-021-01960-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper is devoted to presenting new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved polynomials. The main techniques are based on semialgebraic geometry and variational analysis, which allow us to establish a nonsmooth extension of the seminal Lojasiewicz gradient inequality to regularized gap functions with explicitly calculated exponents.

引用

页码：226 / 247

页数：22

共 50 条

[1] Error Bounds of Regularized Gap Functions for Polynomial Variational Inequalities
Bui Van Dinh
Tien-Son Pham
[J]. Journal of Optimization Theory and Applications, 2022, 192 : 226 - 247
[2] REGULARIZED GAP FUNCTIONS AND ERROR BOUNDS FOR VECTOR VARIATIONAL INEQUALITIES
Charitha, C.
Dutta, Joydeep
[J]. PACIFIC JOURNAL OF OPTIMIZATION, 2010, 6 (03): : 497 - 510
[3] Gap functions and error bounds for quasi variational inequalities
Gupta, Rachana
Mehra, Aparna
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2012, 53 (04) : 737 - 748
[4] Gap Functions and Error Bounds for Variational–Hemivariational Inequalities
Nguyen Van Hung
Stanislaw Migórski
Vo Minh Tam
Shengda Zeng
[J]. Acta Applicandae Mathematicae, 2020, 169 : 691 - 709
[5] Gap functions and error bounds for quasi variational inequalities
Rachana Gupta
Aparna Mehra
[J]. Journal of Global Optimization, 2012, 53 : 737 - 748
[6] GENERALIZED REGULARIZED GAP FUNCTIONS AND ERROR BOUNDS FOR GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES
Asif, Mohd
Khan, Zubair
Babu, Feeroz
Ansari, Abdul Faiz
[J]. Applied Set-Valued Analysis and Optimization, 2022, 4 (01): : 83 - 93
[7] Generalized gap functions and error bounds for generalized variational inequalities
胡艳红
宋文
[J]. Applied Mathematics and Mechanics(English Edition), 2009, 30 (03) : 313 - 321
[8] Gap Functions and Error Bounds for Variational-Hemivariational Inequalities
Hung, Nguyen Van
Migorski, Stanislaw
Tam, Vo Minh
Zeng, Shengda
[J]. ACTA APPLICANDAE MATHEMATICAE, 2020, 169 (01) : 691 - 709
[9] Gap functions and error bounds for generalized vector variational inequalities
Sun, Xiang-Kai
Chai, Yi
[J]. OPTIMIZATION LETTERS, 2014, 8 (05) : 1663 - 1673
[10] Generalized gap functions and error bounds for generalized variational inequalities
Yan-hong Hu
Wen Song
[J]. Applied Mathematics and Mechanics, 2009, 30 : 313 - 321

← 1 2 3 4 5 →