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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.
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Introduction to (modern) Polyhedral Geometry. This lecture defines convex sets and polyhedra and proves a few statements about convex sets and polyhedra.
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High level overview of the simplex method. A proof of correctness for optimality from the simplex method. Introduction to the two phase simplex method.
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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…
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Terminology for simplex method is defined in this lecture. This is written is matrix form. Examples are in the following lectures.
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Review of linear algebra in context of solving linear programs.
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Traveling Salesman problem formulation continued. Discussion of non-negative multipliers, redundant (in)equalities, and their relationship.
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Travelings Sales Man Problem formulation.
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Modeling matching problems in graphs and introducing traveling sales man problem.
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This lecture formulates objective functions for the model in the previous lecture.
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MAT 168 Winter 2024, Lecture 2 - modeling problems in optimization.
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Math 168 Lecture 1, Given on Jan 8th 2024. This lecture gives an introduction to optimization problems and the field of optimization.
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"Identifying and characterizing effectors from the vector-borne emergent pathogen Candidatus Liberibacter solanacearum"
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