Course

Unit 1

Introduction to LPP: Lines and hyperplanes, Convex sets, Convex hull, Formulation of a Linear Programming Problem, Linear Programming Problem; Graphical Method; Simplex method. (10 Hours)

Unit 2

Introduction to optimization: classical optimization, Optimality criteria Necessary and sufficient conditions for existence of optimum point. Fundamental Region Elimination Rules to eliminate a region. One-dimensional Search methods: Golden search method, Fibonacci method, Newtons Method. (12 Hours)

Unit 3

Unconstrained Multivariable optimization: Introduction, Necessary and sufficient conditions for existence of extreme point. Conditions for local minimization. Direct search methods: unidirectional search, box evolutionary search method. (12 Hours)

Unit 4

Gradient-based methods- introduction, the method of steepest descent, Analysis of Newtons Method. Introduction -The Conjugate Direction Algorithm. (12 Hours)

Unit 5

Nonlinear Equality Constrained Optimization- Introduction, Problems with equality constraints Problem Formulation, Lagrange Multiplier Method. Specific Search Algorithms: Hill Climbing, Simulated Annealing, Genetic Algorithms, Ant Colony Optimization. (14 Hours)

Text Books / References

Text Book

1. Edwin K.P. Chong, Stanislaw H. Zak, “An Introduction to Optimization”, 2^nd edition, Wiley, 2013.

Reference Books

1. Mokhtar S. Bazarra, Hamit D Sherali, C.M. Shetty, “Nonlinear programming Theory and applications”, 2^nd edition, Wiley , 2004.
2. Mohan C. Joshi  and  Kannan M.  Moudgalya,  Optimization:  Theory  and  Practice,  Narosa  Publishing House, New Delhi, 2004 (Reference)
3. Kalyanmoy Deb, “Optimization for Engineering Design Algorithms and Examples”, Prentice Hall of India, New Delhi, 2004.
4. S. Rao, “Optimization Theory and Applications”, Second Edition, New Age International (P) Limited Publishers, 1995.
5. Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997.

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