minimization

Numerical Methods for Energy Minimisation: Application to Machine Learning Algorithms

Prof. Charalambos Makridakis, Director of the Institute of Applied and Computational Mathematics of FORTH, Greece

Apr 4, 16:00 - 17:00

B2 L5 R5220

numerical methods energy minimization Applied Machine Learning

In this talk, we discuss problems and numerical methods arising in the calculus of variations and energy minimization. Among numerous applications, energy minimization is a core element of Machine Learning algorithms. Within the field of nonlinear PDEs, the calculus of variations has received a lot of attention from the analysis point of view. Although quite interesting and challenging, the numerical analysis of these problems is much less developed.

Derivative-Free Global Minimization: Relaxation, Monte Carlo and Sampling

Diogo Gomes, Program Chair, Applied Mathematics and Computational Sciences

Nov 27, 11:30 - 12:30

B9 L2 H2 H2

minimization Gradient flows Monte Carlo Monte Carlo Methodology

We develop a derivative-free global minimization algorithm that is based on a gradient flow of a relaxed functional. We combine relaxation ideas, Monte Carlo methods, and resampling techniques with advanced error estimates. Compared with well-established algorithms, the proposed algorithm has a high success rate in a broad class of functions, including convex, non-convex, and non-smooth functions, while keeping the number of evaluations of the objective function small.