PreprintCC BY 4.0arXiv
Duality in Optimization: A Visual Tutorial
Abstract
Lagrangian duality is fundamental to optimization, from the development of solver techniques to the interpretation of solutions; yet its geometric intuition can be difficult to grasp through mathematical derivation alone. This tutorial explains duality and its implications in a highly visual way for a broad audience of students and practitioners. It develops the motivation for the Lagrangian, the two-player game interpretation, and the connection to Fenchel duality. Throughout, it emphasizes the geometric meaning of the solution from both the primal and dual
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BibTeX
@misc{bariya2026duality,
title = {{Duality in Optimization: A Visual Tutorial}},
author = {Mohini Bariya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23751},
eprint = {2609.23751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23751},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Duality in Optimization: A Visual Tutorial
AU - Mohini Bariya
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23751
UR - https://arxiv.org/abs/2609.23751
AB - Lagrangian duality is fundamental to optimization, from the development of solver techniques to the interpretation of solutions; yet its geometric intuition can be difficult to grasp through mathematical derivation alone. This tutorial explains duality and its implications in a highly visual way for a broad audience of students and practitioners. It develops the motivation for the Lagrangian, the two-player game interpretation, and the connection to Fenchel duality. Throughout, it emphasizes the geometric meaning of the solution from both the primal and dual
ER -