CUR decomposition is a low-rank matrix decomposition that is formed using a small number of actual columns and actual rows of the data matrix. Since this decomposition is explicitly constructed using entries from the actual data set, CUR decomposition may be interpretable by practitioners; for this reason, it is sometimes preferable to the Singular Value…

You've probably heard some old guy rant about Newton's method and how it will solve all of your problems: linear, nonlinear, personal, laundry. There's more. In this talk I'll tell you about a way to accelerate plain vanilla fixed point iteration. The first theory for this stuff came from right here in SAS hall and…

In many modeling applications, the analytical structure of fundamental solutions to associated mathematical problems can be exploited to develop more efficient or robust numerical algorithms. I will present several examples of such approaches and techniques based on integral representations arising in the continuum modeling of materials. Some techniques to be discussed include asymptotic analysis, exploiting…

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 of Monte Carlo methods but we will focus on two, namely, Monte Carlo integration and Markov Chain Monte Carlo. Prior knowledge of Monte Carlo methods…

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 therefore needed to characterize data in high dimensional spaces. Considering the parsimonious degrees of freedom of high dimensional data compared to its dimensionality, we study…

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 between convex and nonconvex problems. We will then present the Karush-Kuhn-Tucker optimality conditions. Students who have taken OR 706 (Nonlinear Programming) will find this tutorial…