The talk is divided into two parts. In the first part I will give a short introduction to general(ized) semi-infinite programming (GSIP) and survey the numerical methods. At that we will look at one method in more detail, the transformation-based discretization method. It cleverly combines transforming a GSIP into a usual SIP problem and solving the latter one via discretization and exploiting the lower level convexity of the underlying GSIP problem.
The second part of my talk will focus on the most shimmering application of general semi-infinite optimization, the volume-maximal utilization of (colored) gemstones. There, the task is the following: Given an irregular raw gem which is provided with surface defects and interspersed with inclusions, produce a set of precious gems such that the profit is as high as possible. I will show how this task can be modeled and solved as a general semi-infinite optimization problem, and how we installed a new fully automatic industrial production process for producing the jewels.