


WeylMinkowski's theorem proved using Fourier Motzkin elimination and Polarity of cones.


FourierMotzkin applied to Farkas lemma and duality










Determining the dimension of the face induced by a valid inequality for the stable set problem: Cycle inequality, lifted cycle inequality, clique inequality, edge inequality. notes20201207.pdfThe…


The stable set (independent set) problem: Integer programming formulations, Chvátal–Gomory cuts. notes20201204.pdf Videos and all other materials are copyright 2020 Matthias…


Review: mixed 0/1 modeling. Facility location: Aggregated vs. disaggregated formulation. Strengthening the nogood formulation of logical AND using a Chvátal–Gomory cut. General…


Modeling logical AND using 4 nogood inequalities from the truth table; or using 3 facetdefining inequalities. Mixed 0/1 modeling: Extended formulations of models with fixed charge costs or…


Separation of constraints within a cuttingplane algorithm for solving an LP with exponentially many constraints. Warm starts: Adding a valid inequality to a dictionary by rewriting it in the…


Traveling salesperson problem: Separation of the subtour elimination constraints as a combinatorial optimization problem. TSP formulation using cutset constraints, strengthened cutset constraints,…


Introduction to linear optimization duality. Weak duality theorem. notes20201109.pdf Videos and all other materials are copyright 2020 Matthias Köppe and shared as Open Educational Resources…


Linear optimization problems in standard form. Linear algebra review: Rank of a matrix. Introducing slack variables. Dictionary, basic and nonbasic variables, basic solution. notes20201012.pdf …


Public transport case study: Equality constraint, objective function. Production planning example: Variables, constraints. Review: normal equation of lines in the plane; plotting the feasible region.…
