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Duality

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May 1, 2024 4 minute read

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.

Duality theory has since become a powerful tool in various fields, including economics, finance, and engineering.

Primal and Dual Linear Programs

Path to Duality

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We've curated five courses to help you on your path to Duality. Use these to develop your skills, build background knowledge, and put what you learn to practice.

Sorted from most relevant to least relevant:

Approximation Algorithms Part II

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Master linear programming using graphical and simplex method

Master linear programming using graphical and simplex...

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Machine Learning and AI: Support Vector Machines in Python

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Master Linear Programming with advanced tools

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Optimization: principles and algorithms - Linear optimization

Optimization: principles and algorithms - Linear...

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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.

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

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Nonlinear Optimization

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

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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

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Shrinkage Estimation (Springer Series in Statistics)

Kindle Edition

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