

I teach the continuous part, whereas the discrete part is lead by Martin Loebl.
Schedule of lectures:
(plan) 25.3.  Introduction: Discrete and continuous optimization, their relation, examples (flows in networks). Illustration on linear regression models: different norms, cardinality, signal reconstruction. [chapter 1] 
(plan) 1.4.  Unconstrained optimization: optimality criteria of the first and second order, illustration on the least square problem. Convex sets. [chapter 2, section 3.1] 
(plan) 8.4.  Convex functions, first and second order characterization, chain rules. [sections 3.24] 
(plan) 15.4.  Convex optimization: basic properties of the optimal solutions, characterization of optimality, idea of the ellipsoid method for polynomial problems, [sections 4.1, 4.4.1] 
(plan) 22.4.  An example of copositive programming as a hard subclass. Convex quadratic programming: formulation, complexity, examples. [sections 4.2, 4.4.2, 4.5.2] 
(plan) 29.4.  Convex cone programming: formulation, convex cones, dual cones, the dual problem, weak and strong duality. Cone quadratic programming and semidefinite programming as examples. [section 4.3] 
(plan) 6.5.  KarushKuhnTucker optimality conditions for the equation case, for the general case (with linear independence constraint qualification), and for convex problems (with the Slater condition). [chapter 5] 
(plan) 13.5.  Algorithms. Line search: Armijo rule, Newton method. Unconstraint problems: gradient methods and Newton method. Constraint problems: methods of feasible directions (FrankWolfe, Zoutendijk), penalty and barrier methods. [sections 6.13] 
(plan) 20.5.  Concave programming. Robust optimization with interval and ellipsoidal uncertainty. An application: robust PCA. [chapter 7, section 4.5.1] 
To obtain credits for the tutorial, it is needed to obtain at least 50% of the points of each series of homeworks.
Homeworks: PDF