syllabus - ISYE 7682 Convexity(Fall 2010 Instructor Renato...

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Unformatted text preview: ISYE 7682 Convexity (Fall 2010) Instructor: Renato D.C. Monteiro. Office: Groseclose Bldg 424. Phone #: (404)894-1450. E-mail: [email protected] Office hours: MW 4:00-5:00 Time and Place: MW 5-6:30 on IC 119. Description: In this course I will give an introduction to the theory of convex analysis and its application to optimization. Topics to be covered include: convex sets and convex functions, separation results including Hahn-Banach theorem and Farkas’s lemma, polyhedral theory, polarity and duality relations, normal and tangent cones, subdifferentials and directional derivatives, optimality conditions, Lagrangean and conjugate duality theory, algorithms for solving convex optimization problems such as subgradient methods, bundle methods, Nesterov’s optimal method for smooth problems, Nesterov’s approximation scheme for nonsmooth problems, cutting plane methods and so on. Recomended books: 1. J.-B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms I, Springer-Verlag, 1993. 2. J.-B. Hiriart-Urruty and C. Lemarechal, Fundamental of Convex Analysis, SpringerVerlag, 2001. 3. Yurii Nesterov, Introductory Lectures to Convex Optimization, Kluwer Academic Publishers, 2004. Grading policy: There will be two midterms and one final presentation. Homeworks will be assigned periodically but they will not be graded. Grades will be assigned according to the following weights: exam (70%) and final presentation (30%). Midterm dates: Oct 4 and Nov 29. ...
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