Optimization Problem Formulation, Model Building, Calculus-Based Methods, Convexity and Concavity, Unconstrained Optimization, Constrained Optimization, Linear Programming (LP): Graphical Method, Simplex Method, Duality Theory and Sensitivity Analysis, Applications to Transportation and assignment problems. Nonlinear Programming (NLP):Lagrange Multipliers and Karush-Kuhn-Tucker (KKT) Conditions, Convex Optimization, Nonconvex Optimization Problems, Numerical Optimization Techniques: Line search, Gradient method, Newton's method, conjugate gradient and conjugate direction methods, Advanced Optimization Methods: dynamic programming, integer programming, metaheuristics, Network flows, Interior point methods, Semidefinite optimization, projective and scaling methods for linear programming, Stochastic Optimization Problems, Applications: Signal processing, Machine Learning, Engineering Design and Manufacturing, Transportation and Logistics, Resource Allocation, Financial Modelling, Mention of Genetic algorithm, simulated annealing, Ant Colony and Particle Swarm Optimization, Evolutionary algorithms, Game theory.