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Duality

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May 1, 2024 4 minute read
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Duality is a fundamental concept in mathematics, particularly in linear optimization. It involves the relationship between two linear programs, known as the primal and the dual, where the optimal solution to one program provides valuable information about the optimal solution to the other.

Origins of Duality

The concept of duality was first introduced by the renowned mathematician John von Neumann in the 1940s while working on game theory. Von Neumann recognized the close connection between linear programming and the theory of games.

Path to Duality

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Reading list

We've selected five books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Duality.
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Nonlinear Optimization
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Provides a comprehensive and up-to-date treatment of duality in optimization, including both theoretical and practical aspects.
Nonlinear Optimization
Hardcover
$$$$
Nonlinear Optimization
Kindle Edition
$$$
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Primal-Dual Interior-Point Methods
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Provides a comprehensive and up-to-date treatment of primal-dual interior-point methods, a powerful class of algorithms for solving linear and convex optimization problems.
Primal-Dual Interior-Point Methods
Paperback
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Primal-Dual Interior-Point Methods
Kindle Edition
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Lagrange Multiplier Approach to Variational...
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Provides an introduction to nonlinear optimization with duality theory, including both theoretical and practical aspects.
Lagrange Multiplier Approach to Variational...
Paperback
$$$$
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Mass Religious Ritual and Intergroup Tolerance
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Provides an overview of duality theory in information theory, with a focus on its applications to coding theory and network information theory.
Mass Religious Ritual and Intergroup Tolerance: The...
Hardcover
$$$$
Mass Religious Ritual and Intergroup Tolerance: The...
Kindle Edition
$$$$
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Shrinkage Estimation
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Provides an overview of duality theory in the theory of linear models, with a focus on its applications to statistical inference.
Shrinkage Estimation (Springer Series in Statistics)
Hardcover
$$$$
Shrinkage Estimation (Springer Series in Statistics)
Kindle Edition
$$$$
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