On the Lipschitz stability of weakly Slater systems of convex inequalities (Q2736573)
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scientific article; zbMATH DE number 1644405
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Lipschitz stability of weakly Slater systems of convex inequalities |
scientific article; zbMATH DE number 1644405 |
Statements
10 September 2001
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convex inequalities
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Lipschitz stability
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Hoffman theorem
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bounded excess condition
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On the Lipschitz stability of weakly Slater systems of convex inequalities (English)
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The parametric convex system of inequalities of the form NEWLINE\[NEWLINE f_i(x) \leq \lambda_i, \quad i \in I = \{1,\dots, m\}, \tag{1}NEWLINE\]NEWLINE where the vector \(\lambda \in E_m \) is considered as a parameter, \(f_i: E_n \to E, i \in I\) are complex functions on \(E_n\), is investigated. Two properties of stability of point-set mappings described by the inequalities (1) are discussed. It is shown that if a mapping (connected with Lipschitz and Hoffman conditions) introduced by the convex inequalities (1) with a variable right hand side is satisfying a weak Slater condition then the mapping is stable in Lipschitz sense.NEWLINENEWLINEThese are extensions and refinements of results given in the authors' book [Solvability and stability of problems of polynomial programming (Russian), Izdat. Moskov. Univ., Moscow (1993; Zbl 0805.90096)] and in \textit{D. Klatte}'s paper [Fiacco, Anthony (ed.), Mathematical programming with data perturbations. Lect. Notes Pure Appl. Math. 195, 185--199 (1997; Zbl 0911.90315)]
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