Lecture 5 | Linear Programming & SIMPLEX algorithm w MATLAB | Convex Optimization

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In Lecture 5 of this course on convex optimization, we will be covering Linear Programming and the Simplex algorithm, which was introduced by George Dantzig. The outline of the lecture is as follows:

00:00:00 What is a Linear Program (LP) ?
00:07:24 LP feasible set
00:10:22 LP forms
00:10:50 Standard form LP
00:10:50 Standard form LP
00:11:24 Slack variables
00:13:08 Inequality form LP
00:13:34 Omitting inequality constraints
00:20:38 LP Example: The Diet Problem
00:25:49 The SIMPLEX Algorithm: Method and the usage of Non-basic, Slack, and Artificial variables
00:33:59 The SIMPLEX Algorithm - Example: Iteration 0
00:40:37 The SIMPLEX Algorithm - Example: Iteration 1
00:48:18 The SIMPLEX Algorithm - Example: Iteration 2
00:55:27 The SIMPLEX Algorithm - Example: Iteration 3
01:00:13 MATLAB: Implementing SIMPLEX
01:53:15 MATLAB: Verifying with linprog
01:58:48 George Bernard Dantzig
01:59:12 SIMPLEX: Geometric Interpretation
02:01:09 SIMPLEX: Time Complexity

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Code: https://github.com/therealbazzi/simplex
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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
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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
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YT: https://www.youtube.com/c/AhmadBazzi
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Credits :
Microsoft OneNote: https://products.office.com/en-gb/onenote
MATLAB: https://www.mathworks.com/products/matlab.html

Linear P; lp solver; feasible region in linear programming; slack variable;

#ConvexOptimization #Linear #Program