Shape constraints and algorithms

We consider several problems in the areas of nonparametric regression and image analysis under shape constraints. The task is always to produce simple functions with small number of local extreme values, while multiresolution criteria ensure good approximation of the fitted functions. These strategies easily lead to minimisation problems that can be very difficult to solve, hence the design of efficient algorithms is crucial. One of the problems that we study is concerned with online data where fast processing is particularly important.