Title : Optimization Methods in Sig. Proc. and Comm.
Course No : EE5121
Credits : 4
Prerequisite :

Syllabus :

Convex Analysis

  • Convex sets, cones, inner and outer descriptions
  • Topological properties
  • Polyhedral sets and representations
  • Some main theorems (Caratheodory, Radon, Krein-Milman…)
  • Separating and Supporting Hyperplanes
  • Convex functions, Jensen’s inequality
  • Gradient inequality
  • Maxima and minima of convex functions
  • Sub-gradients

Linear Programming

  • Structural properties, theorem on alternative
  • LP Duality
  • Simplex method
  • Some applications in classification (machine learning), compressed sensing, network flows…

Convex Programming:

  • Convex theorem on alternative
  • Lagrangian and Duality
  • Optimality conditions (KKT, saddle points)
  • Minmax problems, saddle points and game theory interpretation (may be not!)

Basic Algorithms:

  • Gradient descent
  • Sub-gradient, conjugate-gradient
  • Newton’s method, quasi-Newton methods

Text Books :

 

References :