MAT 168 Optimization (Matthias Köppe; Winter 2024)
The following topics are covered in this course:
- Modeling: Examples of optimization problems.
- Graphical method for solving linear programs with 2 variables
- AMPL: a software for modeling and solving linear programs
- Simplex method: dictionary of simplex method, pivoting, ratio test …
- Convex geometry
- Duality, complementary slackness, dual simplex method
- Phase 1 + 2 methods
- Degeneracy + finite termination; the perturbation method
- Assignment problems, network flows
- Integer Programming modeling – fixed costs, Boolean logic, piecewise linear functions, stable set
Videos and all other materials are copyright 2024 Matthias Köppe and shared as Open Educational Resources subject to the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) license.
The following topics are covered in this course:
- Modeling: Examples of optimization problems.
- Graphical method for solving linear programs with 2 variables
- AMPL: a software for modeling and solving linear programs
- Simplex method: dictionary of simplex method, pivoting, ratio test …
- Convex geometry
- Duality, complementary slackness, dual simplex method
- Phase 1 + 2 methods
- Degeneracy + finite termination; the perturbation method
- Assignment problems, network flows
- Integer Programming modeling – fixed costs, Boolean logic, piecewise linear functions, stable set
Videos and all other materials are copyright 2024 Matthias Köppe and shared as Open Educational Resources subject to the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) license.
-
From Acadia Larsen March 12, 2024
-
From Acadia Larsen March 08, 2024
-
From Acadia Larsen March 04, 2024
-
From Acadia Larsen March 04, 2024
-
From Acadia Larsen March 03, 2024
-
From Acadia Larsen February 29, 2024
-
From Acadia Larsen February 26, 2024
Discussion of geometry continues with Carathéodory's theorem and modeling piecewise linear functions with polyhedra. -
From Acadia Larsen February 23, 2024
Continuation of modern geometric descriptions of polyhedrons. Included are definitions of convex polyhedron, half spaces, hyperplanes, affine dimension, and some… -
From Acadia Larsen February 21, 2024
Introduction to (modern) Polyhedral Geometry. This lecture defines convex sets and polyhedra and proves a few statements about convex sets and polyhedra. -
From Acadia Larsen February 15, 2024
Discussion of simplex method with respect to convergence, degeneracy of pivots, pivot rules, and optimality. Improvement of theorems in previous lectures so now we can… -
From Acadia Larsen February 14, 2024
Phase 1 of simplex method and examples with pivot tools. -
From Acadia Larsen February 14, 2024
High level overview of the simplex method. A proof of correctness for optimality from the simplex method. Introduction to the two phase simplex method. -
From Acadia Larsen February 09, 2024
Simplex method computations with a discussion of dictionaries and corresponding solutions. -
From Acadia Larsen February 06, 2024
Terminology and notation for the simplex method. Dictionaries, basis, slack variables, basic feasible solutions and the relationship between these. Certification of… -
From Acadia Larsen February 05, 2024
Terminology for simplex method is defined in this lecture. This is written is matrix form. Examples are in the following lectures.