Linear Optimization |
Jan - Apr 2020 |
Instructor : | B Srivathsan |
TAs : | Ashwani Anand (M.Sc Computer Science, first year) |
A R Sricharan (M.Sc Computer Science, first year) |
Lecture 1 | 06.01.2020 | Linear Programming problem, Examples | Chapters 1 and 2 of [1] |
Lecture 2 | 09.01.2020 | More examples, motivation and introduction to integer linear progamming | Chapter 2 of [1] |
Lecture 3 | 14.01.2020 | Integer linear programming and LP relaxation | Chapter 3 of [1] |
Lecture 4 | 16.01.2020 |
Equational form of LP
Recap of some linear algebra: row rank = col rank |
Chapter 4.1 of [1]
Lectures 1 - 6 of Prof. Sundar's notes [2] |
Lecture 5 | 21.01.2020 | Basic feasible solutions | Chapter 4.2 of [1] |
Lecture 6 | 23.01.2020 | Problem solving session | Problem Set 3 |
28.01.2020 | Quiz 1 | ||
Lecture 7 | 30.01.2020 | An algorithm for solving LP (preparation for simplex) | |
Lecture 8 | 04.02.2020 | Simplex method | Sections 5.1 and 5.2 of [1] |
Lecture 9 | 06.02.2020 | More on simplex: degenerate pivot steps, detecting infeasibility, formalization | Sections 5.3, 5.4 and 5.5 of [1] |
Lecture 10 | 11.02.2020 |
Pivoting rules, Proof of termination when Bland's rule is
used
Convex sets, {x: Ax <= b} is convex, Linear functions |
Sections 5.7, 5.8 of [1]
Lecture 7 from [2] |
Lecture 11 | 18.02.2020 | Extreme points, Optimum occurs at an extreme point | Lectures 8, 9, 10a from [2] |
20.02.2020 | Mid-semester Exam | ||
Lecture 12 | 03.03.2020 | Duality, Proof of duality via simplex | Sections 6.1 and 6.3 of [1] |
Lecture 13 | 05.03.2020 | Exercises in Dualization | Sections 6.2 of [1] |
Lecture 14 | 10.03.2020 | Farkas lemma and its variants | Section 6.4 of [1] |
Lecture 15 | 12.03.2020 | Proof of duality via Farkas' lemma | Section 6.4 of [1] |
Video 1 | 20.03.2020 | Dual of an LP | Link | Section 6.1 of [1] Notes | |
Video 2 | 24.03.2020 | Dual of dual; Writing the duals for different LP forms | Link | Section 6.2 of [1] Notes | |
Video 3 | 26.03.2020 | Proof of duality via Simplex | Link | Section 6.3 of [1] Notes | Assignment 1 (due 31 March 2020, 5 PM) |
Video 4 | 31.03.2020 | Geometric interpretation of duality - Part 1 | Link | Lecture 11 from [2] Notes | |
Video 5 | 02.04.2020 | Geometric interpretation of duality - Part 2 | Link | Lecture 13, 14 from [2] Notes | |
Video 6 | 07.04.2020 | Complementary Slackness | Link | Lecture 15 from [2] Notes | |
09.04.2020 | Assignment 2 (due 16 April 2020, 5 PM) | ||||
Video 7 | 14.04.2020 | Applications of LP: Zero-sum games - Part 1 | Link | Section 8.1 of [1] Notes | |
Video 8 | 16.04.2020 | Applications of LP: Zero-sum games - Part 2 | Link | Section 8.1 of [1] Notes | |
Video 9 | 21.04.2020 | Applications of LP: Zero-sum games - Part 3 | Link | Section 8.1 of [1] Notes |