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Unformatted text preview: Convex Optimization Instructor: Angelia Nedich January 17, 2007 Lecture 1 Outline • What is the Course About • Who Cares and Why • Course Objective • Convex Optimization History • New Interest in the Topic • Formal Introduction Convex Optimization 1 Lecture 1 What is the Course About? • A special class of optimization (includes Linear Programming ) Convex Optimization 2 Lecture 1 Who Cares and Why? • Who? Anyone using or interested in computational aspects of optimization • Why? • To understand the underlying basic terminology, principles, and methodology (to efficiently use the existing software tools) • To develop ability to modify tools when needed • To develop ability to design new algorithms or improve the efficiency of the existing ones Convex Optimization 3 Lecture 1 Course Objective • The goal of this course is to provide you with working knowledge of convex optimizaton • In particular, to provide you with skills and knowledge to • Recognize convex problems • Model problems as convex • Solve the problems Convex Optimization 4 Lecture 1 Convex Optimization History • Convexity Theory and Analysis have being studied for a long time, mostly by mathematicians • Until late 1980’s: • Algorithmic development focused mainly on solving Linear Problems Simplex Algorithm for linear programming (Dantzig, 1947) Ellipsoid Method (Shor, 1970) InteriorPoint Methods for linear programming (Karmarkar, 1984) • Applications in operations research and few in engineering • Since late 1980’s: A new interest in Convex Optimization emerges Convex Optimization 5 Lecture 1...
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 Spring '07
 AngeliaNedich
 Linear Programming, Optimization, Convex Optimization

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