Constrained and Unconstrained Optimization

PRE-REQUISITES: Basic Mathematics

INTENDED AUDIENCE: Any engineering or mathematics student

INDUSTRIES APPLICABLE TO: R&D companies

COURSE OUTLINE: This course has been designed for postgraduate students. Operations research is not only important in its own right but also forms an integral part of applied sciences like economics, management science, engineering design problems etc. The course provides a systematic and thorough discussion on the subject matter with numerous examples.

Lecture 1 : Introduction to Optimization.
Lecture 2 : Assumptions & Mathematical Modeling of LPP.
Lecture 3 : Geometrey of LPP.
Lecture 4 : Graphical Solution of LPP- I.
Lecture 5 : Graphical Solution of LPP- II.
Lecture 6: Solution of LPP: Simplex Method.
Lecture 7: Simplex Method.
Lecture 8: Introduction to BIG-M Method.
Lecture 9: Algorithm of BIG-M Method.
Lecture 10: Problems on BIG-M Method.
Lecture 11: Two Phase Method: Introduction.
Lecture 12: Two Phase Method: Problem Solution.
Lecture 13: Special Cases of LPP.
Lecture 14: Degeneracy in LPP.
Lecture 15: Sensitivity Analysis- I.
Lecture 16: Sensitivity Analysis- II.
Lecture 17: Problems on Sensitivity Analysis.
Lecture 18: Introduction to Duality Theory- I.
Lecture 19: Introduction to Duality Theory- II.
Lecture 20: Dual Simplex Method.
Lecture 21: Examples on Dual Simplex Method.
Lecture 22: Interger Linear Programming.
Lecture 23: Interger Linear Programming.
Lecture 24: IPP: Branch & BBound Method.
Lecture 25: Mixed Integer Programming Problem.
Lecture 26 : Introduction to Transportation Problem - I.
Lecture 27 : Transportation Problem - II.
Lecture 28 : Vogel Approximation Method.
Lecture 29 : Optimal Solution Generation for Transportation Problem.
Lecture 30 : Degeneracy in TP and Overview of Assignment Problem.
Lecture 31 : Introduction to Nonlinear programming.
Lecture 32 : Graphical Solution of NLP.
Lecture 33 : Types of NLP.
Lecture 34 : One dimentional unconstrained optimization.
Lecture 35 : Unconstrained Optimization.
Lecture 36 : Region Elimination Technique-1.
Lecture 37 : Region Elimination Technique-2.
Lecture 38 : Region Elimination Technique-3.
Lecture 39 : Unconstrained Optimization.
Lecture 40 : Unconstrained Optimization.
Lecture 41 : Multivariate Unconstrained Optimization-1.
Lecture 42 : Multivariate Unconstrained Optimization-2.
Lecture 43 : Unconstrained Optimization.
Lecture 44: NLP with Equality Constrained-1.
Lecture 45 : NLP with Equality Constrained-2.
Lecture 46 : Constrained NLP - I.
Lecture 47 : Constrained NLP - II.
Lecture 48 : Constrained Optimization.
Lecture 49 : Constrained Optimization (Contd.).
Lecture 50 : KKT.
Lecture 51 : Constrained Optimization.
Lecture 52 : Constrained Optimization (Contd.).
Lecture 53 : Feasible Direction.
Lecture 54 : Penalty and Barrier Method.
Lecture 55 : Penalty Method.
Lecture 56 : Penalty and Barrier Method.
Lecture 57 : Penalty and Barrier Method (Contd.).
Lecture 58 : Dynamic Programming.
Lecture 59 : Multi - Objective Decision Making.
Lecture 60 : Multi-Attribute Decision Making.