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Optimization Algorithms for Data Analysis

Stephen J Wright (swright***at***cs.wisc.edu)

Abstract: We describe the fundamentals of algorithms for minimizing a smooth nonlinear function, and extensions of these methods to the sum of a smooth function and a convex nonsmooth function. Such objective functions are ubiquitous in data analysis applications, as we illustrate using several examples. We discuss methods that make use of gradient (first-order) information about the smooth part of the function, and also Newton methods that make use of Hessian (second-order) information. Convergence and complexity theory is outlined for each approach.

Keywords: Optimization, Data Analysis

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Applications -- Science and Engineering (Data-Mining )

Citation: To appear in "Mathematics of Data," AMS / Park City Mathematics Institute Series, 2017.

Download: [PDF]

Entry Submitted: 12/01/2016
Entry Accepted: 12/01/2016
Entry Last Modified: 09/10/2017

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