Algorithms for Continuous Optimization - 0365.4414

Lecturer: Prof. Marc Teboulle ( teboulle@post.tau.ac.il )
Office: Schreiber Bldg. 227, Phone: 8896
School of Mathematical Sciences
Tel-Aviv University

Time and Place

Spring Semester, 2012 - Monday 10-13PM, Schreiber Bldg -- Room 209

Intended Audience and Prerequisites

The course will provide an up-to-date introduction to modern optimization algorithms. The advances in computer technology have promoted the field of nonlinear optimization, which has become today an essential tool to solve intelligently complex scientific and engineering problems. All graduate students from Computer Sciences, Engineering, Mathematics, and Statistics are strongly encouraged to register. Previous exposure to a mathematical optimization course is suitable but not a formal preriquisite. A student who had no previous exposure in continuous optimization might still be admitted to the course, after consent of the Lecturer.

Course requirements

The final grade will be determined by a final project. (Theoretical or/and Computational).

Some Useful References

There is no textbook for the course. The material will be based on some of the references below and recent research papers. Some handouts, and all the Lecture Notes will be distributed. However, the students are strongly encouraged to consult the following references (and in particular [1]-[2], and [4]) for further reading and study. References

Approximate syllabus

Smooth Unconstrained Optimization: Classical algorithms and methods of analysis. Gradient type methods. Line search techniques. Newton's type methods, Conjugate Gradients. Rate of convergence Analysis.
Constrained Optimization : Penalty-Barrier methods, Augmented Lagrangian methods, Decomposition schemes.
First Order Methods for Convex Problems: Gradient/Subgradient, Fast Prox-Grad Schemes, Complexity Analysis, Smoothing.
Lagrangian methods for convex optimization: Nonquadratic schemes.
Self-Concordance Theory and Complexity Analysis: Self-concordant functions. Newton's Method Revisited. Polynomial Interior Point Algorithms.
Semidefinite and Conic Programming : Theory, polynomial algorithms, and applications to combinatorial optimization problems and engineering.