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arXiv · 2609.23751

Duality in Optimization: A Visual Tutorial

Mohini Bariya
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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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Mohini Bariya. 2026-09-20. Duality in Optimization: A Visual Tutorial. https://arxiv.org/abs/2609.23751

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