Presenting a strong and clear relationship between theory and
practice, Linear and Integer Optimization: Theory and Practice is
divided into two main parts. The first covers the theory of linear
and integer optimization, including both basic and advanced topics.
Dantzig's simplex algorithm, duality, sensitivity analysis, integer
optimization models, and network models are introduced. More
advanced topics also are presented including interior point
algorithms, the branch-and-bound algorithm, cutting planes,
complexity, standard combinatorial optimization models, the
assignment problem, minimum cost flow, and the maximum flow/minimum
cut theorem. The second part applies theory through real-world case
studies. The authors discuss advanced techniques such as column
generation, multiobjective optimization, dynamic optimization,
machine learning (support vector machines), combinatorial
optimization, approximation algorithms, and game theory. Besides
the fresh new layout and completely redesigned figures, this new
edition incorporates modern examples and applications of linear
optimization. The book now includes computer code in the form of
models in the GNU Mathematical Programming Language (GMPL). The
models and corresponding data files are available for download and
can be readily solved using the provided online solver. This new
edition also contains appendices covering mathematical proofs,
linear algebra, graph theory, convexity, and nonlinear
optimization. All chapters contain extensive examples and
exercises. This textbook is ideal for courses for advanced
undergraduate and graduate students in various fields including
mathematics, computer science, industrial engineering, operations
research, and management science.
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