This is a textbook about linear and integer linear optimization. There
is a growing need in industries such as airline, trucking, and
financial engineering to solve very large linear and integer linear
optimization problems. Building these models requires uniquely trained
individuals. Not only must they have a thorough understanding of the
theory behind mathematical programming, they must have substantial
knowledge of how to solve very large models in today's computing
environment. The major goal of the book is to develop the theory of
linear and integer linear optimization in a unified manner and then
demonstrate how to use this theory in a modern computing environment
to solve very large real world problems. After presenting introductory
material in Part I, Part II of this book is de voted to the theory
of linear and integer linear optimization. This theory is developed
using two simple, but unifying ideas: projection and inverse projec
tion. Through projection we take a system of linear inequalities and
replace some of the variables with additional linear inequalities.
Inverse projection, the dual of this process, involves replacing
linear inequalities with additional variables. Fundamental results
such as weak and strong duality, theorems of the alternative,
complementary slackness, sensitivity analysis, finite basis the
orems, etc. are all explained using projection or inverse projection.
Indeed, a unique feature of this book is that these fundamental
results are developed and explained before the simplex and interior
point algorithms are presented.
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Produktdetaljer
ISBN
9781461549758
Publisert
2020
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter