Mohini Bariya’s arXiv tutorial builds geometric intuition for Lagrangian duality in optimization—bridging solver techniques and solution interpretation with visual explanations of the dual.

Duality in Optimization: A Visual Tutorial

Mohini Bariya
arXiv:2609.23751 [math.OC] (submitted 20 Sep 2026)

Abstract

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

Source

Full paper (PDF): https://arxiv.org/pdf/2609.23751

Canonical abstract page: https://arxiv.org/abs/2609.23751