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.
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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- Fall '08
- Vector Space, Mathematical optimization, Convex function, Convex Optimization, Convex analysis, Convex Analysis and Minimization Algorithms