Linear parametric problems of semi-infinite programming: a continuation method

A one-parameter family of semi-infinite programming (SIP) problems is considered that depends on the parameter $\tau\in[0,\tau^*]$. An analysis of the sensitivity of solutions at a point $\tau=\tau_0\in[0,\tau^*]$ where the solution is nondifferentiable with respect to the parameter is conducted. Rules are described for constructing solutions to a family of SIP problems in a neighborhood of a given point $\tau_0$. A continuation method based on the results obtained is proposed, which uses an active-set strategy.