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Continuation of modern geometric descriptions of polyhedrons. Included are definitions of convex polyhedron, half spaces, hyperplanes, affine dimension, and some connections to Linear Programming.

Introduction to (modern) Polyhedral Geometry. This lecture defines convex sets and polyhedra and proves a few statements about convex sets and polyhedra.

High level overview of the simplex method. A proof of correctness for optimality from the simplex method. Introduction to the two phase simplex method.

Terminology and notation for the simplex method. Dictionaries, basis, slack variables, basic feasible solutions and the relationship between these. Certification of results in terms of the objective…

Terminology for simplex method is defined in this lecture. This is written is matrix form. Examples are in the following lectures.

Review of linear algebra in context of solving linear programs.

Traveling Salesman problem formulation continued. Discussion of non-negative multipliers, redundant (in)equalities, and their relationship.

Travelings Sales Man Problem formulation.

Modeling matching problems in graphs and introducing traveling sales man problem.

This lecture formulates objective functions for the model in the previous lecture.

MAT 168 Winter 2024, Lecture 2 - modeling problems in optimization.

Math 168 Lecture 1, Given on Jan 8th 2024. This lecture gives an introduction to optimization problems and the field of optimization.

"Identifying and characterizing effectors from the vector-borne emergent pathogen Candidatus Liberibacter solanacearum"