Linear parametric semi-infinite programming problems and properties of their solutions in a neighborhood of irregular points

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.