Lecture 15 | Lagrange Dual Problem | Convex Optimization by Dr. Ahmad Bazzi
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5 سال پیش
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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
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Lecture 1 | Introduction to Convex Optimization: Lecture 1 | Convex Optimization | Int...
Lecture 2 | Convex Sets: Lecture 2 | Convex Sets | Convex Opti...
Lecture 3 | Convex Functions: Lecture 3 | Convex Functions | Convex...
Lecture 4 | Convex Optimization Principles : Lecture 4 | Convex Optimization Princ...
Lecture 5 | Linear Programming & SIMPLEX algorithm w MATLAB: Lecture 5 | Linear Programming & SIMP...
Lecture 6 | Quadratic Programs: Lecture 6 | Quadratic Programs | Conv...
Lecture 7 | Quadratically Constrained Quadratic Programs: Lecture 7 | Quadratically Constrained...
Lecture 8 | Second Order Cone Programming: Lecture 8 | Second Order Cone Program...
Lecture 9 | Geometric Programs: Lecture 9 | Geometric Programs (GP) |...
Lecture 10 | Generalized Geometric Programs: Lecture 10 | Generalized Geometric Pr...
Lecture 11 | SemiDefinite Programming Lecture 11 | Semidefinite Programming...
Lecture 12| Vector and Multicriterion Optimization | Pareto Optimal points and the Pareto Frontier Lecture 12 | Vector and Multicriterio...
Lecture 13 | Optimal Trade-off Analysis Lecture 13 | Optimal Trade-off Analys...
Lecture 14 | Lagrange Dual Function Lecture 14 | Lagrange Dual Function |...
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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.
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Instructor: Dr. Ahmad Bazzi
IG: Instagram: 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
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 | Int...
Lecture 2 | Convex Sets: Lecture 2 | Convex Sets | Convex Opti...
Lecture 3 | Convex Functions: Lecture 3 | Convex Functions | Convex...
Lecture 4 | Convex Optimization Principles : Lecture 4 | Convex Optimization Princ...
Lecture 5 | Linear Programming & SIMPLEX algorithm w MATLAB: Lecture 5 | Linear Programming & SIMP...
Lecture 6 | Quadratic Programs: Lecture 6 | Quadratic Programs | Conv...
Lecture 7 | Quadratically Constrained Quadratic Programs: Lecture 7 | Quadratically Constrained...
Lecture 8 | Second Order Cone Programming: Lecture 8 | Second Order Cone Program...
Lecture 9 | Geometric Programs: Lecture 9 | Geometric Programs (GP) |...
Lecture 10 | Generalized Geometric Programs: Lecture 10 | Generalized Geometric Pr...
Lecture 11 | SemiDefinite Programming Lecture 11 | Semidefinite Programming...
Lecture 12| Vector and Multicriterion Optimization | Pareto Optimal points and the Pareto Frontier Lecture 12 | Vector and Multicriterio...
Lecture 13 | Optimal Trade-off Analysis Lecture 13 | Optimal Trade-off Analys...
Lecture 14 | Lagrange Dual Function Lecture 14 | Lagrange Dual Function |...
---------------------------------------------------------------------------------------------------------
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: Instagram: 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
5 سال پیش
در تاریخ 1398/08/19 منتشر شده
است.
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