'Optimization & Applications' (see information & program)
Feb 18 - May 27, 2013
Dr. Michel Baes
V: Tu 10-12
U: Th 15-16
Dr. Christian Wagner
Dr. Apostolos Fertis
V: HG D7.1
U: HG D1.2
plays a central role in the design and analysis of modern and highly
successful algorithms for solving real-world optimization problems. The
lecture (in English) on convex optimization will treat in a balanced
manner theory (convex analysis, optimality conditions) and algorithms
for convex optimization. Beginning with basic concepts and results about
the structure of convex sets, continuity and differentiability of
convex functions (including conjugate functions), the lecture will cover
systems of inequalities, the minimum (or maximum) of a convex function
over a convex set, Lagrange multipliers, duality theory and mini-max
theorems. The course will be illustrated by many applications.
the algorithmic part, we will cover several efficient classes of
optimization methods. We will study Interior-Point Methods, and apply
them to the fastly growing field of semidefinite optimization. We will
show how to use one of the most powerful software to solve efficiently
some semidefinite optimization problems. We will also study several
sugradient-type methods, which are particularly well-designed for very
large convex optimization problems.
The lecture will follow mostly albeit loosely the textbook by S. Boyd and L. Vandenberghe, Convex Optimization, made available on the net (download).
This well-written book covers convex analysis, with a particular emphasis on the interactions between convex analysis and combinatorial optimization problems.
This authoritative work displays a great variety of applications of convex optimization. It constitutes an ideal complement to the book of Boyd and Vandenberghe. Available upon request.
thick book serves as one of the main references for the course. The
authors deal with a number of applications of convex optimization in an
impressive variety of fields. Click on the link to download.
important book emerged from the lecture notes of Pr. Yurii Nesterov. It
focuses on the study of algorithms for convex optimization, and, among
others, interior-point methods. Available upon request.
This well-known book is an excellent reference on linear algebras.
This short book has been developed from a graduate course of Jim Renegar. It contains an original analysis of interior-point methods, which complements beautifully the book of Nesterov. Available upon request.
This is a classical and rather complete reference on convexity. Available upon request.
This book is a collection of well-written reviews on a variety of aspects of semidefinite programming, including a discussion on its numerical behavior and the development of a robustness analysis.
This quite dense work focuses on the question "How efficient can optimization algorithms be ?". Available upon request.
This authoritative but hard book was the first to introduce the concept of self-concordance. It would be difficult to overestimate its importance and its influence on Convex Optimization during the last 15 years.
For Bachelor and Master Students : At least 50% of the marks on the exercises qualifies you for the exam.
For PhD Students : Getting at least 50% of the marks on the exercises and passing the exam. The exam can be replaced by a term project on a topic chosen by the student in agreement with the instructors. If you are interested by a term project, please contact us by March 20. The due date for your report is August 15th, 2012.
Weekly exercises are downloadable every Thursday morning (click on the links at the left of this page). They are due for the next Tuesday at 17h00. You are allowed (and kindly advised) to group in pairs.
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