This tutorial will provide an introduction to nonlinear optimization. We will begin by presenting a general constrained nonlinear program, defining concepts like local versus global optimality, and examining the differences…

High dimensional data exhibit distinct properties compared to its low dimensional counterpart; this causes a common performance decrease and a formidable computational cost increase of traditional approaches. Novel methodologies are…

In this lecture we will present basis theoretical and algorithmic properties of Monte Carlo methods. In particular, their convergence properties and implementational simplicity will be highlighted. There are a variety…