MA5850 Operations Research

Course Details

Linear Optimization: Formulation and Geometrical Ideas of Linear Programming Problems, Simplex Method, Revised Simplex Method, Duality, Sensitivity Analysis, Transportation and Assignment Problems, Introduction to Interior-Point Methods. (Ellipsoid Method, Karmarkar's Method).
Unconstrained optimization of functions of several variables: Basic theory, Classical techniques and numerical methods for unconstrained optimization (Gradient methods, Newton's method, Conjugate Direction methods, and Quasi-Newton methods).
Constrained nonlinear optimization of functions of several variables: Method of Lagrange multipliers, Kuhn-Tucker theory, Convex optimization, Quadratic optimization, Numerical methods for constrained optimization, Dynamic programming.

Course References:

Texts books:
1. E.K.P. Chong, and S.H. Zak: An Introduction to Optimization, 3rd Edn., Wiley Interscience, 2008.
1. D. G. Luenberger, Linear and Nonlinear Programming, 2nd Edn., Kluwer, 2003.
2. N. S. Kambo, Mathematical Programming Techniques, East West Press, 1997.
3. M. S. Bazarra, H.D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd Edn., John Wiley, 1993. (also available as WSE (2004) edition).
4. D.P. Bertsekas, Nonlinear Programming, 2nd Edn., Athena Scientific, 1999.