Summer School 2019

Course Contents

Probability Theory and Stochastic Processes

Probability space, σ-field, random variables, moments, conditional expectations, filtrations, martingales, Markov processes, Markov Chains

Markov Chain Monte Carlo Methods

Optimization with Essential Real Analysis

Basic analyis

Frechet.Gateuax/directional derivatives, first and second order conditions for optimality, McShane proof of KKT conditions

Algorithms for unconstrained optimization: Gradient, conjugate gradient, Newton, quasi-Newton (sketch)

Algorithms for constrained optimization: penalty and barrier functions, projected and reduced gradient, primal-dual, cutting plane (sketch)

Subgradient methods, discrete optimization

Optimization Methods for Machine Learning

Stochastic Optimization

Optimal Transport Problems in Machine Learning

Data Assimilation