On the Continuity of the Optimum Set in Parametric Semiinfinite Programming
Bruno Brosowski · 2020
This chapter assumes that the minimization problem is linear and that the mapping P is in addition upper semicontinuous and compact valued. Here we show that the conditions for lower semicontinuity are also true under weaker assumptions. In particular, we show in Section II that the sufficient conditions for lower semicontinuity of P are still sufficient, if we only assume that P is closed and has locally a bounded selection. Further, we have assumed that the minimization problem is linear. It is well-known that optimization techniques can be used to compute approximate solutions to boundary value problems as well as to compute error bounds for approximate solutions.