"On Gemstones and Maneuverability Problems: Applications of Modern Design Centering Techniques" Oliver Stein (University of Karlsruhe (TH) )
Design centering problems deal with the inscription of a variable body into a fixed container so that, for example, the volume of the body is maximized. Applications include
- the maximal inscription of a gemstone into a rough stone to minimize the wasted material,
- the computation of lower bounds for the volume of complicated container sets by inscription of balls, like in the manoeuvrability problem in robotics, and
- the determination of “innermost points” of sets in order to stay away from their boundaries, like in quality control of production processes.
A numerical solution method for design centering problems with irregular geometrical shapes, in particular in the absence of convexity, is presented. The focus of this method is to produce feasible iterates, that is, each iterate corresponds to a body which is a guaranteed subset of the container. To enforce feasibility, our method constructs certain convex relaxations with ideas from the alpha-BB method of global optimization. Numerical examples illustrate the performance of the method.
Directly after the seminar, the attendants are warmly invited to an "optimization coffee" for discussion.
Slides
