Module 1 (6 Hours)
Mathematical foundations and basic definitions: concepts from linear algebra, geometry, and multivariable calculus.

Module 2 (10 Hours)
Linear optimization: formulation and geometrical ideas of linear programming problems, simplex method, revised simplex method, duality.

Module 3 (6 Hours)
Nonlinear optimization: basic theory, method of Lagrange multipliers, Karush-Kuhn-Tucker theory, convex optimization.

Module 4 (10 Hours)
Numerical optimization techniques: line search, gradient descent, projected gradient descent, sub-gradient descent, accelerated gradient, Newton's method, quasi-Newton methods, stochastic gradient descent, coordinate descent.

Enumerate the fundamental knowledge of linear programming and non-linear programming problems.

to give students the tools and training to recognize convex optimization problems that arise in applications

to give students the background required to use the methods in their own research work or applications

to introduce the numerical optimization techniques.

CO1: To apply the concept of optimization to solve various engineering problems.
CO2: To be able to understand the importance of operation research techniques and mathematical modeling in solving practical problems.
CO3: Analyze characteristics of a general linear programming problem.
CO4: Analyze various methods of solving the unconstrained minimization problem.
CO5: Able to apply various numerical techniques to solve the optimization problem.

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, 4th Ed., 2010. (3nd ed. Wiley India 2008)

E.K.P. Chong and S.H. Zak,, An Introduction to Optimization, 2nd Ed., Wiley, 2010.

D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 3rd Ed., Springer India, 2010