Lecture 16 | Certificate of Suboptimality (ε-suboptimality) | Convex Optimization by Dr. Ahmad Bazzi
19.6 هزار بار بازدید -
4 سال پیش
-
Let's reach 100K subscribers 👉🏻
Let's reach 100K subscribers 👉🏻 https://www.seevid.ir/c/AhmadBazzi?...
In Lecture 16 of this course on Convex Optimization, we talk about a very practical topic, when it comes to numerical optimization algorithms, and that is the ε-suboptimal inequality, which could report how good of an estimate we have. Said differently, the Lagrangian dual feasible points (λ,ν) provides a proof or certificate of the dual gap.
00:00 Intro
01:59 Lagrangian & Dual Functions
03:40 How good of an estimate ? (Certificate)
07:09 ε-suboptimal
10:09 Stopping Criterion
17:23 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 |...
Lecture 15 | Lagrange Dual Problem Lecture 15 | Lagrange Dual Problem | ...
---------------------------------------------------------------------------------------------------------
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 #Certificate #Suboptimal
In Lecture 16 of this course on Convex Optimization, we talk about a very practical topic, when it comes to numerical optimization algorithms, and that is the ε-suboptimal inequality, which could report how good of an estimate we have. Said differently, the Lagrangian dual feasible points (λ,ν) provides a proof or certificate of the dual gap.
00:00 Intro
01:59 Lagrangian & Dual Functions
03:40 How good of an estimate ? (Certificate)
07:09 ε-suboptimal
10:09 Stopping Criterion
17:23 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 |...
Lecture 15 | Lagrange Dual Problem Lecture 15 | Lagrange Dual Problem | ...
---------------------------------------------------------------------------------------------------------
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 #Certificate #Suboptimal
4 سال پیش
در تاریخ 1399/02/27 منتشر شده
است.
19,629
بـار بازدید شده