Lecture 14 | Lagrange Dual Function | Convex Optimization by Dr. Ahmad Bazzi скачать в хорошем качестве

Lecture 14 | Lagrange Dual Function | Convex Optimization by Dr. Ahmad Bazzi

☕️ Buy me a coffee: https://paypal.me/donationlink240 🙏🏻 Support me on Patreon:   / ahmadbazzi   In Lecture 14 of this course on Convex Optimization, we introduce the Lagrangian duality theory. In essence, for each optimization problem (convex or not), we can associate a certain function referred to as the Lagrangian function. This function, in turn, has a dual function (which serves as an infimum over the variable of interest x). It turns out that, for any optimisation problem, the dual function is a lower bound on the optimal value of the optimisation problem in hand. This lecture focuses on many examples that derive the Lagrangian and the associated dual functions. MATLAB implementations are also presented to give useful insights. This lecture is outlined as follows: 00:00 Intro 01:00 Lagrangian function and duality 04:02 Lagrangian dual function 06:46 Lower bound on the optimal value 09:16 MATLAB: Lower bound verification 15:28 Example 1 - Least Squares 17:48 Example 2 - Linear Programming 20:48 Example 3 - Two-way Partitioning 26:04 Relationship between conjugate function and the dual function 31:22 Example 4 - Equality Constrained Norm minimization 33:37 Example 5 - Entropy Maximization 35:44 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 | ...   --------------------------------------------------------------------------------------------------------- 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