Lecture 15 | Lagrange Dual Problem | Convex Optimization by Dr. Ahmad Bazzi

☕️ Buy me a coffee: https://paypal.me/donationlink240 🙏🏻 Support me on Patreon:   / ahmadbazzi   In Lecture 15 of this course on Convex Optimization, we talk about a very very important topic in convex optimisation that is the Lagrange Dual Problem. This lecture is outlined as follows: 00:00:00 Intro 00:00:44 Revision: Lagrange Dual Function 00:01:30 The Dual Problem 00:06:54 Example 1: Dual Problem of Standard LP 00:08:59 Example 2: Dual Problem of Inequality LP 00:13:59 Weak Duality 00:16:24 Example 3: The 2-way Partitioning Problem (Revisited) 00:21:42 Strong Duality 00:23:15 Slater’s Condition 00:24:32 What is a Relative Interior (Convex Analysis by Tyrell Rockefellar) ? 00:28:16 Generalization of Slater’s Condition 00:29:26 Example 4: Duality of LS problems 00:38:33 Example 5: Duality of LP problems 00:54:52 Example 6: Duality of QCQP problems 00:59:22 Example 7 : Duality of the Entropy Maximization Problem 01:03:48 Example 8 : Duality of the Trust Region Problem (non-convex problem) 01:11:51 Outro --------------------------------------------------------------------------------------------------------- Lecture 1 | Introduction to Convex Optimization:    • Lecture 1 | Convex Optimization | Introduc...   Lecture 2 | Convex Sets:    • Lecture 2 | Convex Sets | Convex Optimizat...   Lecture 3 | Convex Functions:    • Lecture 3 | Convex Functions | Convex Opti...   Lecture 4 | Convex Optimization Principles :    • Lecture 4 | Convex Optimization Principles...   Lecture 5 | Linear Programming & SIMPLEX algorithm w MATLAB:    • Lecture 5 | Linear Programming & SIMPLEX a...   Lecture 6 | Quadratic Programs:    • Lecture 6 | Quadratic Programs | Convex Op...   Lecture 7 | Quadratically Constrained Quadratic Programs:    • Lecture 7 | Quadratically Constrained Quad...   Lecture 8 | Second Order Cone Programming:    • Lecture 8 | Second Order Cone Programming ...   Lecture 9 | Geometric Programs:    • Lecture 9 | Geometric Programs (GP) | Conv...   Lecture 10 | Generalized Geometric Programs:    • Lecture 10 | Generalized Geometric Program...   Lecture 11 | SemiDefinite Programming    • Lecture 11 | Semidefinite Programming (SDP...   Lecture 12| Vector and Multicriterion Optimization | Pareto Optimal points and the Pareto Frontier    • Lecture 12 | Vector and Multicriterion Opt...   Lecture 13 | Optimal Trade-off Analysis    • Lecture 13 | Optimal Trade-off Analysis | ...   Lecture 14 | Lagrange Dual Function    • Lecture 14 | Lagrange Dual Function | Conv...   --------------------------------------------------------------------------------------------------------- References: [1] Boyd, Stephen, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004. [2] Nesterov, Yurii. Introductory lectures on convex optimization: A basic course. Vol. 87. Springer Science & Business Media, 2013. Reference no. 3: [3] Ben-Tal, Ahron, and Arkadi Nemirovski. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. Vol. 2. Siam, 2001. --------------------------------------------------------------------------------------------------------- Instructor: Dr. Ahmad Bazzi IG:   / drahmadbazzi   FB: https://www.facebook.com/profile.php?... RG: https://www.researchgate.net/profile/... MSE: https://math.stackexchange.com/users/... YT:    / ahmadbazzi   --------------------------------------------------------------------------------------------------------- Credits : Microsoft OneNote: https://products.office.com/en-gb/one... #ConvexOptimization #Lagrange #Dual