Lecture 21 | Weak Alternatives | Convex Optimization by Dr. Ahmad Bazzi
22.1 هزار بار بازدید -
4 سال پیش
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In Lecture 21 of this course on Convex Optimization, we talk about the theorem of weak alternatives of general optimization problems.
This lecture is outlined as follows:
00:00 Introduction
04:02 Feasibility Problem
05:41 Optimization Feasibility Problem
07:55 Dual Function
08:41 Note on Strong Alternatives
10:43 Dual Problem
13:12 Weak Duality
13:41 Relating (S) with (T)
15:16 Weak Alternatives
17:31 Why Weak Alternatives ?
19:33 Summary
23:18 Outro
Lecture Notes: https://bazziahmad.com/2020/11/28/wea...
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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 |...
Lecture 15 | Lagrange Dual Problem Lecture 15 | Lagrange Dual Problem | ...
Lecture 16 | Certificate of Suboptimality Lecture 16 | Certificate of Suboptima...
Lecture 17 | Complementary Slackness Lecture 17 | Complementary Slackness ...
Lecture 18 | KKT Conditions Lecture 18 | KKT Conditions | Convex ...
Lecture 19 | Perturbation and Sensitivity Analysis Lecture 19 | Perturbation and Sensiti...
Lecture 20 | Equivalent Reformulations Lecture 20 | Equivalent Reformulation...
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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 #EquivalentReformulation #Dual
In Lecture 21 of this course on Convex Optimization, we talk about the theorem of weak alternatives of general optimization problems.
This lecture is outlined as follows:
00:00 Introduction
04:02 Feasibility Problem
05:41 Optimization Feasibility Problem
07:55 Dual Function
08:41 Note on Strong Alternatives
10:43 Dual Problem
13:12 Weak Duality
13:41 Relating (S) with (T)
15:16 Weak Alternatives
17:31 Why Weak Alternatives ?
19:33 Summary
23:18 Outro
Lecture Notes: https://bazziahmad.com/2020/11/28/wea...
---------------------------------------------------------------------------------------------------------
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 |...
Lecture 15 | Lagrange Dual Problem Lecture 15 | Lagrange Dual Problem | ...
Lecture 16 | Certificate of Suboptimality Lecture 16 | Certificate of Suboptima...
Lecture 17 | Complementary Slackness Lecture 17 | Complementary Slackness ...
Lecture 18 | KKT Conditions Lecture 18 | KKT Conditions | Convex ...
Lecture 19 | Perturbation and Sensitivity Analysis Lecture 19 | Perturbation and Sensiti...
Lecture 20 | Equivalent Reformulations Lecture 20 | Equivalent Reformulation...
---------------------------------------------------------------------------------------------------------
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 #EquivalentReformulation #Dual
4 سال پیش
در تاریخ 1399/09/08 منتشر شده
است.
22,171
بـار بازدید شده