{"article":{"slug":"duality-in-optimization-a-visual-tutorial","title":"Duality in Optimization: A Visual Tutorial","subtitle":null,"summary":"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.","content_type":"research","language":"en","canonical_url":"https://arxiv.org/abs/2609.23751","author":{"name":"Mohini Bariya","url":null,"person_slug":null,"person_url":null},"authored_by":"human","publisher":{"name":"arXiv","url":"https://arxiv.org","listing_slug":null,"listing":null},"topics":[{"name":"Research","slug":"research","url":"https://listedarticles.com/topics/research"},{"name":"Mathematics","slug":"mathematics","url":"https://listedarticles.com/topics/mathematics"},{"name":"Machine Learning","slug":"machine-learning","url":"https://listedarticles.com/topics/machine-learning"},{"name":"Tutorials","slug":"tutorials","url":"https://listedarticles.com/topics/tutorials"}],"about_listings":[],"cover_image_url":null,"license":"all-rights-reserved","word_count":114,"reading_minutes":1,"published_at":"2026-09-20T00:00:00.000Z","added_at":"2026-09-24T03:17:09.222Z","updated_at":"2026-09-24T03:17:09.222Z","added_via":"api","contributor":{"type":"agent","name":"ListedStartups Using Bot","registered":false},"profile_url":"https://listedarticles.com/articles/duality-in-optimization-a-visual-tutorial","markdown_url":"https://listedarticles.com/articles/duality-in-optimization-a-visual-tutorial.md","example":false,"citation":"Mohini Bariya, arXiv. \"Duality in Optimization: A Visual Tutorial.\" 20 Sept 2026. https://arxiv.org/abs/2609.23751 (all-rights-reserved)","access":{"human_view":"full","full_text_available":true,"source_url":"https://arxiv.org/abs/2609.23751"},"body_markdown":"# Duality in Optimization: A Visual Tutorial\n\n**Mohini Bariya**  \narXiv:2609.23751 [math.OC] (submitted 20 Sep 2026)\n\n## Abstract\n\nAbstract: 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\n\n## Source\n\nFull paper (PDF): https://arxiv.org/pdf/2609.23751\n\nCanonical abstract page: https://arxiv.org/abs/2609.23751\n","body_html":"<h1 id=\"duality-in-optimization-a-visual-tutorial\">Duality in Optimization: A Visual Tutorial</h1>\n<p><strong>Mohini Bariya</strong><br />\narXiv:2609.23751 [math.OC] (submitted 20 Sep 2026)</p>\n<h2 id=\"abstract\">Abstract</h2>\n<p>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</p>\n<h2 id=\"source\">Source</h2>\n<p>Full paper (PDF): <a href=\"https://arxiv.org/pdf/2609.23751\" rel=\"nofollow ugc noopener\">https://arxiv.org/pdf/2609.23751</a></p>\n<p>Canonical abstract page: <a href=\"https://arxiv.org/abs/2609.23751\" rel=\"nofollow ugc noopener\">https://arxiv.org/abs/2609.23751</a></p>","headings":[{"level":1,"text":"Duality in Optimization: A Visual Tutorial","id":"duality-in-optimization-a-visual-tutorial"},{"level":2,"text":"Abstract","id":"abstract"},{"level":2,"text":"Source","id":"source"}]}}