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

☕️ Buy me a coffee: https://paypal.me/donationlink240 🙏🏻 Support me on Patreon: https://www.patreon.com/c/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: https://youtu.be/SHJuGASZwlE Lecture 2 | Convex Sets: https://youtu.be/QV5qtTq1Tro Lecture 3 | Convex Functions: https://youtu.be/XzW-B1CJ_ao Lecture 4 | Convex Optimization Principles : https://youtu.be/aMC3WPGMLes Lecture 5 | Linear Programming & SIMPLEX algorithm w MATLAB: https://youtu.be/dAyeNmz6p-c Lecture 6 | Quadratic Programs: https://youtu.be/kM52hSvBY4k Lecture 7 | Quadratically Constrained Quadratic Programs: https://youtu.be/SP2-7AG2wfk Lecture 8 | Second Order Cone Programming: https://youtu.be/sVbcJx4g-LQ Lecture 9 | Geometric Programs: https://youtu.be/PoLKyYsmVD0 Lecture 10 | Generalized Geometric Programs: https://youtu.be/Lio9kxMYbRk Lecture 11 | SemiDefinite Programming https://youtu.be/XwyE8vIszo4 Lecture 12| Vector and Multicriterion Optimization | Pareto Optimal points and the Pareto Frontier https://youtu.be/iUAxxsz1Axw Lecture 13 | Optimal Trade-off Analysis https://youtu.be/YtGFNsZ0RVc Lecture 14 | Lagrange Dual Function https://youtu.be/Qneah_lyQ0o --------------------------------------------------------------------------------------------------------- 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: https://www.instagram.com/drahmadbazzi/ FB: https://www.facebook.com/profile.php?... RG: https://www.researchgate.net/profile/... MSE: https://math.stackexchange.com/users/... YT: https://www.youtube.com/c/AhmadBazzi --------------------------------------------------------------------------------------------------------- Credits : Microsoft OneNote: https://products.office.com/en-gb/one... #ConvexOptimization #Lagrange #Dual