Module sgpp::optimization
Optimization of smooth sparse grid interpolants.
This SG⁺⁺ module was developed as part of a Master's thesis with the translated title
"Hierarchical Optimization with Gradient-Based Methods on Sparse Grid Functions".
In the thesis, a new approach for minimizing objective functions
is developed.
It can be summarized in three steps:
- Adaptive iterative sparse grid generation. Two methods are implemented for generating adaptively a sparse grid according to the function values at the grid points.
- B-spline or Mexican-Hat hierarchization. The objective function is interpolated by a linear combination of sufficiently smooth sparse grid basis functions.
- Gradient-based optimization of the smooth interpolant. Various optimization methods, gradient-based as well gradient-free ones, are implemented for optimizating the sparse grid surrogate.