Discrete and Continuous Optimization (summer 2017)
Time and Place
Lecture: Thursdays 14:00 to 15:30 in S9
Tutorial: Thursdays 15:40 to 17:10 in S6
Office hours:
By email appointment.
Topics
Introduction to mathematical optimization (> 13.4.2017)
Unconstrained optimization
First and second order optimality conditions
Least square method (< 13.4.2017)
Convexity (> 20.4.2017)
Convex sets
Convex Functions (< 20.4.2017)
First and second order characterizations (> 28.4.2017)
Convex Optimization
Basic properties (< 28.4.2017)
Quadratic programming (> 4.5.2017)
Cone programming
Duality (< 4.5.2017)
Cone quadratic programming (> 11.5.2017)
Semidefinite programming (< 11.5.2017)
Computational complexity
The good case: ellipsoid method (> 18.5.2017)
The bad case: copositive programming
Karush-Kuhn-Tucker optimality conditions
Equation case
General case (< 18.5.2017)
Algorithms (> 25.5.2017)
Line search: Armijo rule
Unconstrained problems: Gradient method
Constrained problems
Methods of feasible directions
Penalty and barrier methods (< 25.5.2017)
Literature
S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
D. Luenberger and Ye. Linear and Nonlinear Programming. Springer, New York, third edition, 2008.
M. S. Bazaraa, H. D. Sherali, and C. M. Shetty. Nonlinear Programming. Theory and Algorithms. 3rd ed. John Wiley & Sons., NJ, 2006.
Other links
First half of the lecture held by Hans Raj Tiwary
F. Augugliaro, A.P. Schoellig, and R. D’Andrea, Generation of collision-free trajectories for a quadrocopter fleet: A sequential convex programming approach, EEE/RSJ International Conference on Intelligent Robots and Systems, 2012: pp. 1917–1922.