General information on the course
Suggested textbooks:
- S. Boyd, L. Vandenberghe, Convex optimization, Cambridge University Press, 2004
- M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear programming: theory and algorithms, Wiley & Sons, 2006 (Chapters 1-6, 8-9)
- J. Nocedal, S. Wright, Numerical Optimization, Springer Series in Operations Research and Financial Engineering, 2006 (Chapters 1-3, 5, 12, 16, 17)
- J. Gondzio, Interior point methods 25 years later, European Journal of Operational Research, vol. 218 (2012), pp. 587-601
- A.R. Conn, K. Scheinberg, L.N. Vicente, Introduction to Derivative-Free Optimization, SIAM series on Optimization, 2009 (Chapters 1, 7)
- N. Cristianini, J. Shawe-Taylor, An Introduction to Support Vector Machines, Cambridge University Press, 2004.
- A.J. Smola, B. Scholkopf, A tutorial on support vector regression, Statistics and Computing, vol. 14 (2004), pp. 199-222.
- M. Teboulle, A Unified Continuous Optimization Framework for Center-Based Clustering Methods, Journal of Machine Learning Research, vol. 8 (2007), pp. 65-102.
- D.T. Luc, Theory of Vector Optimization, Springer, 1989 (Chapters 2, 4)
- Y. Sawaragi, H. Nakayama, T. Tanino, Theory of Multiobjective Optimization, Academic Press, 1985 (Chapters 3, 7)
- M.J. Osborne, A. Rubinstein, A Course in Game Theory, MIT press, 1994 (Chapters 1-4)
- N. Nisan, T. Roughgarden, E. Tardos, V.V. Vazirani, Algorithmic Game Theory, Cambridge University Press, 2007 (Chapter 3)
Slides:
- 0 – Introduction
- 1 – Preliminaries on convex sets and convex functions
- 2 – Existence of optimal solutions and optimality conditions
- 3 – Lagrangian duality
- 4 – Support Vector Machines for classification problems
- 5 – Regression problems
- 6 – Clustering problems
- 7 – Solution methods for unconstrained optimization problems
- 8 – Solution methods for constrained optimization problems
- 9 – Multiobjective optimization problems
- 10 – Noncooperative game theory
Exercises:
- MATLAB cheat sheet
- Ch. 2-3 – Nonlinear optimization theory
- Ch. 3: Lagrangian dual of a nonconvex problem
- Ch. 4 – SVM for classification problems:
- Ch. 5 – Regression problems:
- Ch. 6 – Clustering problems:
- Ch. 7 – Solution methods for unconstrained optimization:
- Ch. 8 – Solution methods for constrained optimization:
- Ch. 9 – Multiobjective optimization:
- Ch. 10 – Noncooperative game theory:
Further exercises: