Search for tag: "formulation"

2020-12-09-b: Convex piecewise linear modeling (MAT 168 Optimization)

Modeling convex piecewise linear functions in a data science application (ℓ1 regression). notes-2020-12-09-b.pdf Videos and all other materials are copyright 2020 Matthias Köppe and shared as…

From  Matthias Koeppe on December 9th, 2020 0 likes 5 plays 0  

2020-12-09-a: Modeling with convex multipliers (MAT 168 Optimization)

Modeling with convex multipliers. notes-2020-12-09-a.pdf Videos and all other materials are copyright 2020 Matthias Köppe and shared as Open Educational Resources subject to the Creative…

From  Matthias Koeppe on December 7th, 2020 0 likes 13 plays 0  

2020-12-04: Stable set problem, formulations/cuts (MAT 168 Optimization)

The stable set (independent set) problem: Integer programming formulations, Chvátal–Gomory cuts. notes-2020-12-04.pdf Videos and all other materials are copyright 2020 Matthias…

From  Matthias Koeppe on December 4th, 2020 0 likes 16 plays 0  

2020-12-02: Facility location, Chvatal-Gomory cuts (MAT 168 Optimization)

Review: mixed 0/1 modeling. Facility location: Aggregated vs. disaggregated formulation. Strengthening the no-good formulation of logical AND using a Chvátal–Gomory cut. General…

From  Matthias Koeppe on December 2nd, 2020 0 likes 17 plays 0  

2020-11-30: Logical and mixed 0/1 modeling (MAT 168 Optimization)

Modeling logical AND using 4 no-good inequalities from the truth table; or using 3 facet-defining inequalities. Mixed 0/1 modeling: Extended formulations of models with fixed charge costs or…

From  Matthias Koeppe on November 30th, 2020 0 likes 21 plays 0  

2020-11-23: Cutting plane algorithms (MAT 168 Optimization)

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

From  Matthias Koeppe on November 23rd, 2020 0 likes 17 plays 0  

2020-11-20: TSP formulations: strength, relaxations (MAT 168 Optimization)

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

From  Matthias Koeppe on November 20th, 2020 0 likes 18 plays 0  

2020-11-18: Traveling salesperson problem (TSP)

Back to modeling: The (symmetric, metric) traveling salesperson problem (TSP) in the natural IP formulation. Subtour elimination constraints. Modeling with exponentially many constraints. Constraint…

From  Matthias Koeppe on November 18th, 2020 0 likes 19 plays 0  

2020-10-21: LP reformulations, geometry (MAT 168 Optimization)

The operation of introducing slack variables as an "extended formulation". Reformulating problems with free variables to obtain a problem in standard form, viewed as another extended…

From  Matthias Koeppe on October 21st, 2020 0 likes 31 plays 0