Mathematical Foundations (Concepts from Linear Algebra, Geometry, and Multivariable Calculus)

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.

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.