The need to characterise and compute subsets of finite and infinite dimensional spaces is ubiquitous in applied mathematics. The last decades have witnessed the successful development of numerical algorithms for the computer aided approximation of attractors, reachable sets, viability kernels and solution sets of inverse problems. Popular software packages are based on cell discretisation, densities of invariant measures and level-set methods, each having their individual strengths and weaknesses.
The subject of generalised convexity is well-developed in the context of optimisation theory as a straightforward extension of convex optimisation and Fenchel duality. Furthermore, this concept allows the design of set spaces containing sets with particular geometric or smoothness properties, which may be regarded as the natural spaces in which certain sets evolve or solutions of inverse problems are to be found.
The aim of this workshop is to bring together a core of experts for the existing approaches to set computation, from generalised convexity and from bilevel optimisation to exchange ideas and assess in which way set computation can benefit from the idea of set spaces and the theory of generalised convexity.Key topics. The themes for this workshop include