Title: Advanced topics in Networks

Course No: EE6151

Credits  3

Prerequisite: Basic convex optimization course (for example EE5121) which introduces convex functions, optimization, duality and hopefully SDP’s

Syllabus:

  1. Recap of convex optimization
    1. Convex functions
    2. Duality (Conic)
  2. Complexity bounds
  3. Unconstrained minimization (smooth  functions)
    1. Gradient descent
    2. Newtons method
  4. Constrained minimization  (smooth  functions)
  5. Interior point techniques (smooth convex functions)
  6. Subgradient methods (non-smooth functions)
    1. Subgradients
    2. Subgradient  methods (constrained)
    3. Stochastic subgradient
  7. Cutting plane methods
    1. Ellipsoid method
  8. Proximal algorithms
  9. FISTA
  10. Mirror descent algorithm

 

Reference books

 

  1. Introductory lectures on convex optmization, A basic course, Yurii Nesterov
  2. Convex optimization, Stephen Boyd
  3. Lectures on modern convex optimization, Aharon Ben-Tal and Arkadi Nemirovski
  4. Theory of convex optimization for machine learning, Sebastien Bubeck
  5. Convex optimization theory, Dimitri P Bertsekas
  6. Nonlinear programming, Dimitri P Bertsekas
  7. Linear and nonlinear programming, David G, Luenberger and Yinyu Ye
  8. Numerical optimization, Jorge Nocedal and Stephen J. Wright
  9. Problem complexity and method efficiency in optimization, A Nemirovsky and D. B. Yudin
  10. A course in convexity, Alexander Barvinok