Applied Optimization for Geometry Processing

Countless techniques in geometry processing can be described variationally, that is, as the minimization or maximization of an objective function measuring shape properties. Algorithms for parameterization, mapping, quad meshing, alignment, smoothing, and other tasks can be expressed and solved in this powerful language. With this motivation in mind, this talk will cover important classes of optimization problems and corresponding algorithms to solve them. In particular I will discuss the fundamentals, advantages and drawbacks of widely used algorithms like Active Set and Interior-Point methods for constrained optimization as well as Branch-and-Bound techniques for mixed-integer optimization problems. All these algorithms will be motivated and explained geometrically such that important concepts, as for instance convexity, are clarified from an intuitive point of view. The main goal of this talk is to offer a practical introduction to the area of advanced optimization that helps new users to master crucial design choices.