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Welcome to Linear Optimization! The field of study of
linear optimization (or linear programming, LP) is the
fundamental branch of optimization, with applications
to many areas including life sciences, computer
science, defense, finance, telecommunications,
transportation, etc. Other types of optimization
typically use LP as the underlying model. This course
will provide an integrated view of the theory,
solution techniques, and applications of linear
optimization. There will be a fair bit of emphasis on
theorems and their proofs. The treatment of most
topics will begin with a geometric point of view,
followed by the development of the solution techniques
(algorithms), which are described using linear
algebra. A background in linear algebra and
multivariate calculus is assumed. Topics covered
include linear programming formulations, geometry of
linear programming, the simplex method, duality,
sensitivity analysis, interior point methods, and
integer programming basics. Apart from problems
involving proofs, the student will use Matlab (or
another programming language, e.g., Python) for
implementing some of the computations and
algorithms. A state-of-the-art modeling software such
as
AMPL
will also be introduced for solving problems modeling
real life situations.
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