111104027 Mathematics Linear programming and Extensions Prof. Prabha Sharma Video IIT Kanpur Select
Lecture_01_Introduction to Linear Programming Problems.
Lecture_02_ Vector space, Linear independence and dependence, basis.
Lec_03_Moving from one basic feasible solution to another, optimality criteria.
Lecture_04_Basic feasible solutions, existence & derivation.
Lecture_5_Convex sets, dimension of a polyhedron, Faces, Example of a polytope.
Lecture_6_Direction of a polyhedron, correspondence between bfs and extreme points.
Lecture_7_Representation theorem, LPP solution is a bfs, Assignment 1.
Lecture_08_Development of the Simplex Algorithm, Unboundedness, Simplex Tableau.
Lecture_9_ Simplex Tableau & algorithm ,Cycling, Bland�s anti-cycling rules, Phase I & Phase II.
Lecture_10_ Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs.
Lecture_11_Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP.
Lecture_12_LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem.
Lecture_13_Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of duality.
Lecture_14_Examples of writing the dual, complementary slackness theorem.
Lecture_15_Complementary slackness conditions, Dual Simplex algorithm, Assignment 3.
Lecture_16_Primal-dual algorithm.
Lecture_17_Problem in lecture 16, starting dual feasible solution, Shortest Path Problem.
Lecture_18_Shortest Path Problem, Primal-dual method, example.
Lecture_19_Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vector.
Lecture_20_ Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysis.
Lecture_21_Parametric LPP-Right hand side vector.
Lecture_22_Parametric cost vector LPP.
Lecture_23_Parametric cost vector LPP, Introduction to Min-cost flow problem.
Lecture_24_Mini-cost flow problem-Transportation problem.
Lecture_25_Transportation problem degeneracy, cycling
Lecture_26_ Sensitivity analysis.
Lecture_27_ Sensitivity analysis.
Lecture_28_Bounded variable transportation problem, min-cost flow problem.
Lecture_29_Min-cost flow problem
Lecture_30_Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solution
Lecture_31_Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cycles.
Lecture_32_ Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis.
Lecture_33_Min-cost flow changes in arc capacities , Max-flow problem, assignment 7
Lecture_34_Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm.
Lecture_35_Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem.
Lecture_36_Improved Max-flow algorithm.
Lecture_37_Critical Path Method (CPM).
Lecture_38_Programme Evaluation and Review Technique (PERT).
Lecture_39_ Simplex Algorithm is not polynomial time- An example.
Lecture_40_Interior Point Methods .
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