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Vol. 49 No. 1–3 (2023)
Serdica Mathematical Journal

Articles

An upper bound for a condition number theorem of variational inequalities

https://doi.org/10.55630/serdica.2023.49.33-48

Published 20-11-2023

  • Tullio Zolezzi

Tullio Zolezzi
University of Genoa, Italy

Abstract

Nonlinear variational inequalities in Banach spaces are considered. A notion of (absolute) condition number with respect to the right-hand side is introduced. A distance among variational inequalities is defined. We prove that the distance to suitably restricted ill-conditioned variational inequalities is bounded from above by a multiple of the reciprocal of the condition number. By using an analogous lower bound of the companion paper [14], we obtain a full condition number theorem for variational inequalities. The particular case of convex optimization problems is also considered. Known results dealing with optimization problems are thereby generalized.

2020 Mathematics Subject Classification:

49J40, 49K40, 49J53, 90C31

Keywords

variational inequalities, condition number theorems, conditioning in convex optimization

Full text

Author Details

Tullio Zolezzi

Retired from DIMA
University of Genoa
via Dodecaneso 35
16146 Genoa, Italy
e-mail: zolezzi@dima.unige.it

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