Course Description

Constrained and unconstrained optimization methods and their applications in data analysis.

Additional Requirements for Graduate Students:
Graduate students will be required to submit additional, more extensive homework problems and/or projects, requiring a deeper synthesis of the concepts and material.

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Athena Title

Optimization and Data Analysis

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Prerequisite

(MATH 3000 or MATH 3300 or MATH 3300E or MATH 3500 or MATH 3500H) and (MATH 2270 or MATH 2270E or MATH 2500 or MATH 2500E or MATH 3510 or MATH 3510H)

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Semester Course Offered

Offered spring

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Grading System

A - F (Traditional)

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Course Objectives

Students will learn about the basic types of optimization problems that arise in applications, especially in data analysis. Students will learn about the standard approaches to solving these problems and will be able to implement these approaches in an applied setting.

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Topical Outline

Spectral Theorem and Singular Value Decomposition, Image Compression Vector Space Norms and Matrix Norms Eckart – Young Theorem Least Squares and Pseudoinverse Gradient Methods, Hessians Stochastic Gradient Descent Convexity Newton’s Method Linear Programming and the Simplex Method Soft Thresholding, Basis Pursuit Compressed Sensing Graphs, Laplacians, and Spectral Clustering Nonlinear Constraints, Lagrange Multipliers, MinMax Neural Networks, Deep Learning

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