caa a22 4500 445842377 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00245-010-9118-5 doi (NATIONALLICENCE)springer-10.1007/s00245-010-9118-5 On Implicit Active Constraints in Linear Semi-Infinite Programs with Unbounded Coefficients [Elektronische Daten] [M. Goberna, G. Lancho, M. Todorov, V. VeradeSerio] 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. Springer Science+Business Media, LLC, 2010 Linear semi-infinite programming nationallicence Implicit active constraints nationallicence Extended active constraints nationallicence Locally upper bounded systems nationallicence Strongly unique solution nationallicence Stability nationallicence Goberna M. Dep. of Statistics and Operations Research, Alicante University, 03071, Alicante, Spain aut Lancho G. Instituto de Física y Matemáticas, Universidad Tecnológica de Mixteca, Carretera a Acatlima Km.2.5, Huajuapan de Leon, Oaxaca, Mexico aut Todorov M. Dep. of Physics and Mathematics, UDLA, 72820, San Andrés Cholula, Puebla, Mexico aut VeradeSerio V. Facultad de Ciencias Económicas, Instituto de Ciencias Básicas, Universidad Nacional de Cuyo, 5500, Mendoza, Argentina aut Applied Mathematics & Optimization Springer-Verlag 63/2(2011-04-01), 239-256 0095-4616 63:2<239 2011 63 245 https://doi.org/10.1007/s00245-010-9118-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-010-9118-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goberna M. Dep. of Statistics and Operations Research, Alicante University, 03071, Alicante, Spain aut NATIONALLICENCE 700 1- Lancho G. Instituto de Física y Matemáticas, Universidad Tecnológica de Mixteca, Carretera a Acatlima Km.2.5, Huajuapan de Leon, Oaxaca, Mexico aut NATIONALLICENCE 700 1- Todorov M. Dep. of Physics and Mathematics, UDLA, 72820, San Andrés Cholula, Puebla, Mexico aut NATIONALLICENCE 700 1- VeradeSerio V. Facultad de Ciencias Económicas, Instituto de Ciencias Básicas, Universidad Nacional de Cuyo, 5500, Mendoza, Argentina aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 63/2(2011-04-01), 239-256 0095-4616 63:2<239 2011 63 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer