About Error Bounds in Metrizable Topological Vector Spaces

被引：0
作者：
Malek Abbasi
Michel Théra
机构：
[1] University of Isfahan,Department of Mathematics
[2] XLIM UMR-CNRS 7252,undefined
[3] Université de Limoges,undefined
[4] France and Centre for Informatics and Applied Optimisation,undefined
[5] Federation University Vic,undefined
来源：
Set-Valued and Variational Analysis | 2022年 / 30卷 / 4期
关键词：
Error bound; Hoffman estimate; Hadamard directional derivative; Translation invariant metric; Strongly regular point; Homogeneously continuous functions; 49J52; 49J53; 49J99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper aims to present some sufficient criteria under which a given function between two spaces that are either topological vector spaces whose topologies are generated by metrics or metrizable subsets of some topological vector spaces, satisfies the error bound property. Then, we discuss the Hoffman estimation and obtain some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows to calculate the coefficient of the error bound. The applications of this presentation are illustrated by some examples.
引用
收藏
页码：1291 / 1311
页数：20
相关论文
共 22 条
[1]  
Peña J(2021)New characterizations of Hoffman constants for systems of linear constraints Math. Program. 187 79-109
[2]  
Vera JC(2022)Error bounds revisited Optimization 0 1-33
[3]  
Zuluaga LF(1973)Bounds for error in the solution set of a perturbed linear program Linear Algebra Appl. 6 69-81
[4]  
Cuong ND(1977)A characterization of stability in linear programming Operations Res. 25 435-447
[5]  
Kruger AY(1996)A unified analysis of Hoffman’s bound viaFenchel duality SIAM J. Optim. 6 265-282
[6]  
Robinson S(2002)On the sensitivity analysis of Hoffman constants for systems of linear inequalities SIAM J. Optim. 12 913-927
[7]  
Robinson S(2000)Hoffman’s error bound, local controllability, and sensitivity analysis SIAM J. Control Optim. 38 947-970
[8]  
Burke J(1979)Regular points of Lipschitz functions Trans. Amer. Math. Soc. 251 61-69
[9]  
Tseng P(1979)Necessary and sufficient conditions for a local minimum. I. A reduction theorem and first order conditions SIAM J. Control Optim. 17 245-250
[10]  
Azé D(1934)On conditional extrema of functionals Math. Sbornik 41 390-401
123