Metric regularity of semi-infinite constraint systems
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Title: | Metric regularity of semi-infinite constraint systems |
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Authors: | Cánovas Cánovas, María Josefa | Dontchev, Asen L. | López Cerdá, Marco A. | Parra López, Juan |
Research Group/s: | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Semi-infinite programming | Metric regularity | Distance to inconsistency | Conditioning |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | Nov-2005 |
Publisher: | Springer Berlin Heidelberg |
Citation: | Mathematical Programming. 2005, 104(2-3): 329-346. doi:10.1007/s10107-005-0618-z |
Abstract: | We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F+g is not metrically regular is equal to the reciprocal to the modulus of regularity of F. The Lyusternik-Graves theorem gives a straightforward extension of these results to nonlinear systems. We also discuss the distance to infeasibility for homogeneous semi-infinite linear inequality systems. |
Sponsor: | Research partially supported by grants BFM2002-04114-C02 (01-02) from MCYT (Spain) and FEDER (E.U.), GV04B-648 and GRUPOS04/79 from Generalitat Valenciana (Spain), and Bancaja-UMH (Spain). |
URI: | http://hdl.handle.net/10045/75151 |
ISSN: | 0025-5610 (Print) | 1436-4646 (Online) |
DOI: | 10.1007/s10107-005-0618-z |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Springer-Verlag Berlin Heidelberg 2005 |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s10107-005-0618-z |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
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2005_Canovas_etal_MathProgramm_final.pdf | Versión final (acceso restringido) | 220,17 kB | Adobe PDF | Open Request a copy |
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