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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 1980s: 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 1980s: A new interest in Convex Optimization emerges Convex Optimization 5 Lecture 1...
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 Spring '07
 AngeliaNedich

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