Optimality criterion for semi-infinite programming problems with faithfully convex constraint functions
Problemy fiziki, matematiki i tehniki, no. 1 (2017), pp. 47-53.

Voir la notice de l'article provenant de la source Math-Net.Ru

Convex semi-infinite programming problem with polyhedral index sets and faithfully convex constraint functions are considered. An explicit optimality criterion is formulated and proved for the given class of problems. A comparative analysis of this criterion with known optimality conditions is performed. An illustrative example is presented.
Keywords: semi-infinite programming, convex programming, immobility order, faithfully convex function.
Mots-clés : immobile index
@article{PFMT_2017_1_a7,
     author = {O. I. Kostyukova and M. V. Kulagina},
     title = {Optimality criterion for semi-infinite programming problems with faithfully convex constraint functions},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {47--53},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_1_a7/}
}
TY  - JOUR
AU  - O. I. Kostyukova
AU  - M. V. Kulagina
TI  - Optimality criterion for semi-infinite programming problems with faithfully convex constraint functions
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2017
SP  - 47
EP  - 53
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2017_1_a7/
LA  - ru
ID  - PFMT_2017_1_a7
ER  - 
%0 Journal Article
%A O. I. Kostyukova
%A M. V. Kulagina
%T Optimality criterion for semi-infinite programming problems with faithfully convex constraint functions
%J Problemy fiziki, matematiki i tehniki
%D 2017
%P 47-53
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2017_1_a7/
%G ru
%F PFMT_2017_1_a7
O. I. Kostyukova; M. V. Kulagina. Optimality criterion for semi-infinite programming problems with faithfully convex constraint functions. Problemy fiziki, matematiki i tehniki, no. 1 (2017), pp. 47-53. http://geodesic.mathdoc.fr/item/PFMT_2017_1_a7/

[1] M. Lopez, G. Still, “Semi-infinite programming: theory, methods and applications”, European Journal of Operational Research, 180 (2007), 491–518 | DOI | MR | Zbl

[2] A. Shapiro, “Semi-infinite programming, duality, discretization and optimality conditions”, Optimization, 58:2 (2009), 133–161 | DOI | MR | Zbl

[3] O. Stein, G. Still, “On optimality conditions for generalized semi-infinite programming problems”, Journal of Optimization Theory and Applications, 104:2 (2000), 443–458 | DOI | MR | Zbl

[4] O. I. Kostyukova, T. V. Tchemisova, S. A. Yermalinskaya, “Study of a Special Nonlinear Problem Arising in Convex Semi-Infinite Programming”, Journal of Mathematical Sciences, 161:6 (2009), 878–892 | DOI | MR

[5] D. Klatte, “Stable local minimizers in semiinfinite optimization: regularity and second-order conditions”, J. Comput. Appl. Math., 56 (1994), 137–157 | DOI | MR | Zbl

[6] A. Moldovan, L. Pellegrini, “On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions”, Journal of Optimization Theory and Applications, 142 (2009), 165–183 | DOI | MR | Zbl

[7] O. I. Kostyukova, T. V. Tchemisova, S. A. Yermalinskaya, “On the algorithm of determination of immobile indices for convex SIP problems”, International Journal on Mathematics and Statistics, 13:8 (2008), 13–33 | MR | Zbl

[8] O. I. Kostyukova, T. V. Tchemisova, “Implicit optimality criterion for convex SIP problem with box constrained index set”, Journal of Mathematical Sciences, 20 (2012), 475–502 | MR | Zbl

[9] R. T. Rockafellar, “Some convex programs whole duals are linearly constrained”, Nonlinear Programming, eds. J. B. Rosen, O. L. Mangasarian, K. Ritter, Academic Press, New York, 1970, 293–322 | DOI | MR

[10] O. I. Kostyukova, T. V. Tchemisova, A constructive algorithm for determination of immobile indices in convex SIP problems with polyhedral index sets, Preprint, Institute of Mathematics, National Academy of Sciences of Belarus, Mathematical Department, University of Aveiro, Aveiro, 2012, 17 pp. | MR

[11] M. V. Kulagina, “Algoritm opredeleniya nepodvizhnykh indeksov v vypuklykh zadachakh polubeskonechnogo programmirovaniya s mnogogrannym mnozhestvom indeksov”, Problemy fiziki, matematiki i tekhniki, 2014, no. 3(20), 65–76

[12] O. I. Kostyukova, T. V. Tchemisova, “Convex SIP Problems with Finitely Representable Compact Index Sets: Immobile Indices and the Properties of the Auxiliary NLP Problem”, Set-Valued and Variational Analysis, 23 (2015), 519–546 | DOI | MR | Zbl