On implicit active constraints in linear semi-infinite programs with unbounded coefficients
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Title: | On implicit active constraints in linear semi-infinite programs with unbounded coefficients |
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Authors: | Goberna, Miguel A. | Lancho Romero, Guillermo Arturo | Todorov, Maxim I. | Vera de Serio, Virginia N. |
Research Group/s: | Programación Semi-infinita |
Center, Department or Service: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad Tecnológica de Mixteca. Instituto de Física y Matemáticas | Universidad de las Américas Puebla. Departamento de Física y Matemáticas | Universidad Nacional de Cuyo. Facultad de Ciencias Económicas |
Keywords: | Linear semi-infinite programming | Implicit active constraints | Extended active constraints | Locally upper bounded systems | Strongly unique solution | Stability |
Knowledge Area: | Estadística e Investigación Operativa |
Issue Date: | 21-Sep-2010 |
Publisher: | Springer |
Citation: | GOBERNA TORRENT, Miguel Ángel, et al. “On implicit active constraints in linear semi-infinite programs with unbounded coefficients”. Applied Mathematics & Optimization. Online First (21 Sept. 2010). ISSN 0095-4616 |
Abstract: | The concept of implicit active constraints at a given point provides useful local information about the solution set of linear semi-infinite systems and about the optimal set in linear semi-infinite programming provided the set of gradient vectors of the constraints is bounded, commonly under the additional assumption that there exists some strong Slater point. This paper shows that the mentioned global boundedness condition can be replaced by a weaker local condition (LUB) based on locally active constraints (active in a ball of small radius whose center is some nominal point), providing geometric information about the solution set and Karush-Kuhn-Tucker type conditions for the optimal solution to be strongly unique. The maintaining of the latter property under sufficiently small perturbations of all the data is also analyzed, giving a characterization of its stability with respect to these perturbations in terms of the strong Slater condition, the so-called Extended-Nürnberger condition, and the LUB condition. |
Sponsor: | MICINN of Spain, Grant MTM2008-06695-C03-01, CONACyT of MX.Grant 55681 and SECYT-UNCuyo of Argentina, Grant Res. 1094/09-R. |
URI: | http://hdl.handle.net/10045/15405 |
ISSN: | 0095-4616 (Print) | 1432-0606 (Online) |
DOI: | 10.1007/s00245-010-9118-5 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | The original publication is available at www.springerlink.com |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1007/s00245-010-9118-5 |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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Goberna_On_implicit_active_constraints_Rev.pdf | Versión revisada (acceso libre) | 198,39 kB | Adobe PDF | Open Preview |
Goberna_On_implicit_active_constraints_Final.pdf | Versión final (acceso restringido) | 477,24 kB | Adobe PDF | Open Request a copy |
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