Num Optim for AI Data Sci

3 Credits · Level: Graduate, Undergraduate

Optimization is central to any problem involving decision making, whether in engineering or economics. The task of decision making entails choosing between various alternatives. This choice is governed by our desire to make the ”best” decision. The measure of goodness of the alternatives is described by an objective function or performance index. Optimization theory and methods deal with selecting the best alternative in the sense of the given objective function. The area of optimization has received enormous attention in recent years, primarily because of the rapid progress in computer technology. The main objective of this course is to provide working knowledge on various types of optimization problems including linear and nonlinear program, constrained/unconstrained, smooth/nonsmooth optimization problems. Some of the most recent approaches such as alternating minimization, operator splitting, penalty methods will be discussed. Practical applications in image/signal processing, medical imaging, and data analysis may be discussed. Suggested textbook: Numerical Optimization, Jorge Nocedal and Stephen J. Wright, Second Edition, 2006 (textbook is not required). Prerequisite: MATH 504.