Geodesic
Linear parametric semi-infinite programming problems and properties of their solutions in a neighborhood of irregular points
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 5, pp. 775-791

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A one-parametric family of semi-infinite programming problems depending on a parameter $\tau\in[0,\tau^*]$ is considered. The sensitivity of the solution at an arbitrary point $\tau=\tau_0\in[0,\tau^*]$ is analyzed. Rules for the construction of solutions to this family for $\tau$ from a neighborhood of the point $\tau_0$ are described. The differentiability of the solutions with respect to the parameter is examined, and rules for the calculation of one-sided derivatives are presented. 
@article{ZVMMF_2005_45_5_a2,
     author = {E. A. Kostina and O. I. Kostyukova},
     title = {Linear parametric semi-infinite programming problems and properties of their solutions in a neighborhood of irregular points},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {775--791},
     publisher = {mathdoc},
     volume = {45},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_5_a2/}
}
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E. A. Kostina; O. I. Kostyukova. Linear parametric semi-infinite programming problems and properties of their solutions in a neighborhood of irregular points. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 5, pp. 775-791. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_5_a2/