Convex Optimization (NMMB409) - Winter term 2026/27

Lecture: Monday 12:20 - 13:50, K2. Wednesday 10:40 - 12:10, K8.
Practicals: Wednesday 12:20 - 15:50, K8., run by Max Hadek

Literature: Evaluation:
Zápočet: To obtain the credit (zápočet) one needs to be positive on 2 out of 3 tests in the exercise classes.
Exam: oral examination. It is necessary to have obtained the credit (zápočet) in order to take the exam.

Consulation: If you have any questions, do not hesitate to ask! Longer discussions best in my office hour, Mo: 14:00-15:30.

Overview:

Date Topics Reference Practicals
28.9 no lecture! (St. Wenceslas Day)
30.9 Examples, historic overview; linear (and convex) programs can be solved efficiently
Pr: Basic examples in CVXPY		 [MG2],[BV1] Ex1, Code
5.10 LP relaxations (Job Assignment Example). Def: half-spaces, convex polyhedra and their vertices; LPs in equational form [MG3.2, 4]
7.10 Basic feasible solutions of LPs in equational form as candidates for optima; simplex tableaus
Pr:Convex sets, LPs		 [MG4, 5.1] Ex2
12.10 The Simplex Method + exception handling (unboundedness/degeneracy/infeasibility).
The problem of cycling; various Pivot rules (largest coefficient/increase, steepest edge)		 [MG5]
14.10 Bland's rule against cycling, the complexity of Simplex algorithms; basic convex sets
Pr: LPs and simplex method, Max' LP visualiser		 [MG5]
[BV2.1-2.2]		 Ex3
19.10 Convex sets, separating and supporting hyperplane theorem, generalized inequalities
important examples of convex functions		 [BV2,3.1]
21.10 Convex functions: first+second order criterion, epigraph, operations preserving convexity
Pr: Examples		 [BV3] Ex4
26.10 Composition rules; quasiconvex functions
local=global optima for convex problems, first-order criterion for optimal solutions		 [BV3]
[BV4.1-4.2]
28.10 no lecture/practical! (Independent Czechoslovak State Day)
2.11
4.11 Ex5
9.11
11.11 Ex6
16.11
18.11 Ex7
23.11
25.11 Ex8
30.11
2.12 Ex9
7.12
9.12 Ex10
14.12
16.12 Ex11
4.1
6.1 Ex12