# Linear programming and Extensions Video Lectures

Linear programming and Extensions
'Linear programming and Extensions' Video Lectures by Prof. Prabha Sharma from IIT Kanpur
 "Linear programming and Extensions" - Video Lectures 1. Lecture_01_Introduction to Linear Programming Problems. 2. Lecture_02_ Vector space, Linear independence and dependence, basis. 3. Lec_03_Moving from one basic feasible solution to another, optimality criteria. 4. Lecture_04_Basic feasible solutions, existence & derivation. 5. Lecture_5_Convex sets, dimension of a polyhedron, Faces, Example of a polytope. 6. Lecture_6_Direction of a polyhedron, correspondence between bfs and extreme points. 7. Lecture_7_Representation theorem, LPP solution is a bfs, Assignment 1. 8. Lecture_08_Development of the Simplex Algorithm, Unboundedness, Simplex Tableau. 9. Lecture_9_ Simplex Tableau & algorithm ,Cycling, BlandÂ’s anti-cycling rules, Phase I & Phase II. 10. Lecture_10_ Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs. 11. Lecture_11_Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP. 12. Lecture_12_LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem. 13. Lecture_13_Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of duality. 14. Lecture_14_Examples of writing the dual, complementary slackness theorem. 15. Lecture_15_Complementary slackness conditions, Dual Simplex algorithm, Assignment 3. 16. Lecture_16_Primal-dual algorithm. 17. Lecture_17_Problem in lecture 16, starting dual feasible solution, Shortest Path Problem. 18. Lecture_18_Shortest Path Problem, Primal-dual method, example. 19. Lecture_19_Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vector. 20. Lecture_20_ Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysis. 21. Lecture_21_Parametric LPP-Right hand side vector. 22. Lecture_22_Parametric cost vector LPP. 23. Lecture_23_Parametric cost vector LPP, Introduction to Min-cost flow problem. 24. Lecture_24_Mini-cost flow problem-Transportation problem. 25. Lecture_25_Transportation problem degeneracy, cycling 26. Lecture_26_ Sensitivity analysis. 27. Lecture_27_ Sensitivity analysis. 28. Lecture_28_Bounded variable transportation problem, min-cost flow problem. 29. Lecture_29_Min-cost flow problem 30. Lecture_30_Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solution 31. Lecture_31_Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cycles. 32. Lecture_32_ Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis. 33. Lecture_33_Min-cost flow changes in arc capacities , Max-flow problem, assignment 7 34. Lecture_34_Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm. 35. Lecture_35_Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem. 36. Lecture_36_Improved Max-flow algorithm. 37. Lecture_37_Critical Path Method (CPM). 38. Lecture_38_Programme Evaluation and Review Technique (PERT). 39. Lecture_39_ Simplex Algorithm is not polynomial time- An example. 40. Lecture_40_Interior Point Methods .
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