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Linear Programming and Extensions. Instructor: Prof. Prabha Sharma, Department of Mathematics and Statistics, IIT Kanpur.

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September 23, 2023

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September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Certificate of completion

Unlimited Duration

Description

Linear Programming and Extensions. Instructor: Prof. Prabha Sharma, Department of Mathematics and Statistics, IIT Kanpur.

The objective of this course is to introduce those real life problems which can be formulated as Linear Programming Problems (LPP). The course will be taught as a first course in optimization, hence all the concepts will be properly motivated and explained with examples. Topics covered in this course include Simplex algorithm; Duality theory and its ramifications; Basic ideas of the ellipsoid algorithm and Karmarkar's algorithm; Special cases of LPP; and Dynamic programming and PERT/CPM algorithms. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction to Linear Programming Problems Unlimited
  • Lecture 02 – Vector Space, Linear Independence and Dependence, Basis Unlimited
  • Lecture 03 – Moving from One Basic Feasible Solution to Another, Optimality Criteria Unlimited
  • Lecture 04 – Basic Feasible Solutions, Existence and Derivation Unlimited
  • Lecture 05 – Convex Sets, Dimension of a Polyhedron Faces, Example of a Polytope Unlimited
  • Lecture 06 – Direction of a Polyhedron, Correspondence between BFS and Extreme Points Unlimited
  • Lecture 07 – Representation Theorem, LPP Solution is a BFS Unlimited
  • Lecture 08 – Development of the Simplex Algorithm, Unboundedness, Simplex Tableau Unlimited
  • Lecture 09 – Simplex Tableau and Algorithm, Cycling, Bland’s Anti-Cycling Rules Unlimited
  • Lecture 10 – Big-M Method, Graphical Solutions, Adjacent Extreme PTS and Adjacent BFS Unlimited
  • Lecture 11 – Progress of Simplex Algorithm on a Polytope, Bounded Variables LPP Unlimited
  • Lecture 12 – LPP Bounded Variable, Revised Simplex Algorithm, Duality Theory Unlimited
  • Lecture 13 – Weak Duality Theorem, Economic Interpretation of Dual Variables Unlimited
  • Lecture 14 – Examples of Writing the Dual Complementary Slackness Theorem Unlimited
  • Lecture 15 – Complementary Slackness Conditions, Dual Simplex Algorithm Unlimited
  • Lecture 16 – Primal-Dual Algorithm Unlimited
  • Lecture 17 – Starting Dual Feasible Solutions, Shortest Path Problem Unlimited
  • Lecture 18 – Shortest Path Problem, Primal-Dual Method Unlimited
  • Lecture 19 – Shortest Path Problem-Complexity, Interpretation of Dual Variables Unlimited
  • Lecture 20 – Post-Optimality Analysis, Changes in B, Adding a New Constraint Unlimited
  • Lecture 21 – Parametric LPP-Right Hand Side Vector Unlimited
  • Lecture 22 – Parametric Cost Vector LPP Unlimited
  • Lecture 23 – Parametric Cost Vector LPP, Introduction to Min-Cost Flow Problem Unlimited
  • Lecture 24 – Min-Cost Flow Problem, Transportation Problem Unlimited
  • Lecture 25 – Transportation Problem Degeneracy, Cycling Unlimited
  • Lecture 26 – Sensitivity Analysis Unlimited
  • Lecture 27 – Sensitivity Analysis (cont.) Unlimited
  • Lecture 28 – Bounded Variable Transportation Problem, Min-Cost Flow Problem Unlimited
  • Lecture 29 – Min-Cost Flow Problem Unlimited
  • Lecture 30 – Starting Feasible Solution, Lexicographic Method for Preventing Cycling Unlimited
  • Lecture 31 – Shortest Path Problem, Shortest Path between Any Two Nodes Unlimited
  • Lecture 32 – Min-Cost-Flow Sensitivity Analysis, Shortest Path Problem Sensitivity Analysis Unlimited
  • Lecture 33 – Min-Cost Flow Changes in ARC Capacities, Max-Flow Problem Unlimited
  • Lecture 34 – Min-Cut Max-Flow Theorem, Labelling Algorithm Unlimited
  • Lecture 35 – Max-Flow-Critical Capacity of an ARC, Starting Solution for Min-Cost Flow Problem Unlimited
  • Lecture 36 – Improved Max-Flow Algorithm Unlimited
  • Lecture 37 – Critical Path Method (CPM) Unlimited
  • Lecture 38 – Programme Evaluation and Review Technique (PERT) Unlimited
  • Lecture 39 – Simplex Algorithm is not Polynomial Time – An example Unlimited
  • Lecture 40 – Interior Point Methods Unlimited

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