Mathematical foundations.

Unconstrained optimization of functions of several variables, Classical techniques, Numerical methods for unconstrained optimization.

Linear Optimization: Simplex method, Revised simplex method, Ellipsoid method, Karmarkar's method, Duality and sensitivity, Transportation and Assignment problems.

Constrained optimization of functions of several variables, Lagrange multipliers, Kuhn-Tucker theory, Numerical methods for constrained optimization, Convex optimization, Quadratic optimization, Dynamic programming.

Software Support: MATLAB, MATHEMATICA, OR packages.

Textbook: (that I will be following for most parts)
E.K.P. Chong, and S.H. Zak: An Introduction to Optimization, 2nd Edn., Wiley, 2001 (also available as WSE (2004) edition).

Other Texts and References:
R. Fletcher, Practical Methods of Optimization, 2nd Edn., John Wiley, 1987.
D. G. Luenberger, Linear and Nonlinear Programming, 2nd Edn., Kluwer, 2003.
N. S. Kambo, Mathematical Programming Techniques, East West Press, 1997.
M. S. Bazarra, J.J. Jarvis, and H.D. Sherali, Linear Programming and Network Flows, 2nd Edn., John Wiley, 1990. (also available as WSE (2003) edition).
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).
D.P. Bertsekas, A. Nedic, and A. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, 2003.
D.P. Bertsekas, Nonlinear Programming, 2nd Edn., Athena Scientific, 1999.