Module I [ 10 h]
Introduction: Optimization problem formulation (design variables, constraints, objective function, variable bounds), classification of optimization problems.
Single Variable Optimization Algorithms: Analytical Method, Bracketing Methods (Exhaustive Search Method and Bounding Phase Method) Region Elimination Methods (Interval Halving Method, Fibonacci Search Method and Golden Section Search Method), Gradient-based Methods (Newton-Raphson Method, Bisection Method, Secant Method).
Module II [ 6 h]
Multivariable Optimization Algorithms: Analytical Method, Direct Search Method: Hooke-Jeeves Pattern Search Method, Gradient-based Methods (Cauchy's Steepest Descent Method, Newton’s Method, Marquardt’s method).
Module III [ 12 h]
Constrained Optimization Algorithms: Kuhn-Tucker conditions, Penalty Function Method, Method of Multipliers, Cutting Plane mMthod, Generalized Reduced Gradient method
Module IV [ 8 h]
Nature Inspired Algorithms: global optima, Genetic Algorithm, Simulated Annealing

This course deals with various numerical methods used for single objective optimization problems.

Such methods have application in finding solution to many engineering problems.

It explains the traditional methods for searching local optima and a few non-traditional methods for finding global optima.

Upon completion of this theory course, the student will be able to
CO1: solve unconstrained single variable optimization problems
CO2: solve unconstrained multi-variable optimization problems
CO3: solve constrained optimization problems
CO4: solve optimization problems using nature-inspired algorithms
CO5: use computer software in solving all the above types of optimization problems

Deb, Kalyanmoy, Optimization for Engineering Design : Algorithms and Examples, 2e, PHI , 2024

Rao, SS, Engineering Optimization : Theory and Practice, 3e, New Age International , 2024

Arora, Jasbir S, Introduction to Optimum Design, 4e, Academic Press , 2023

Alam, SN Islam, S and Patel, SK, Advanced Guide to MATLAB: Practical Examples in Science and Engineering, IK International , 2022