MATH-504: Integer optimisation

Lectures in this course (31)

Covers integer programming, dynamic programming, and optimal solutions complexity.

Covers Dognion's Theorem, explaining the proof of infeasible Integer Programming problems.

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Explores the Steinitz Lemma and the concept of cycles in linear algebra.

Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.

Explores dynamic programming with the Steinitz sequence to optimize solutions efficiently.

Covers Doignon's theorem in integer programming, stating that a set is minimally infeasible if the removal of any constraint makes it feasible.

Covers the Subset Sum problem and the efficient LLL algorithm for finding solutions in lattice basis reduction.

Explores lattices, Minkowski's Theorem, and properties of symmetric convex sets.

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Covers the LLL algorithm for reducing lattice bases to shorter and more orthogonal forms through iterative transformations.

Page 2 of 2