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An Introduction to Duality in Convex Optimization

ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality conditions, such as the complementary slackness and Karush-Kuhn-Tucker conditions are presented. Finally, three di↵erent examples illustrate the power of the Lagrangian duality. They are solved by using the optimality conditions previously introduced.