Introduction: Optimization – optimal problem formulation, engineering optimization problems, optimization algorithms, numerical search for optimal solution.

Single Variable optimization: Optimality criteria, bracketing methods – exhaustive search method, bounding phase method- region elimination methods – interval halving, Fibonacci search, golden section search, point estimation method- successive quadratic search, gradient based methods.

Multivariable Optimization: Optimality criteria, unconstrained optimization – solution by direct substitution, unidirectional search – direct search methods evolutionary search method, simplex search method, Hook-Jeeves pattern search method, gradient based methods – steepest descent, Cauchy’s steepest descent method, Newton’s method, conjugate gradient method – constrained optimization. Kuhn-Tucker conditions.

• S.S. Rao, “Optimization Theory and Applications”, Second Edition, New Age International (P) Limited Publishers, 1995

• Kalyanmoy Deb, “Optimization for Engineering Design Algorithms and Examples”, Prentice Hall of India, New Delhi, 2004.
• Edwin K.P. Chong and Stanislaw H. Zak, “An Introduction to Optimization”, Second Edition, Wiley-Interscience Series in Discrete Mathematics and Optimization, 2004.
• M. Asghar Bhatti, “Practical Optimization Methods: with Mathematics Applications”, Springer Verlag Publishers, 2000.

Evaluation Pattern

Objectives

• To understand the concept of search space and optimality for solutions of engineering problems.
• To understand some computation techniques for optimizing single variable functions.
• To carry out various computational techniques for optimizing severable variable functions.

Course Outcomes

• CO1: Understand different types of Optimization Techniques in engineering problems. Learn Optimization methods such as Bracketing methods, Region elimination methods, Point estimation methods.
• CO2: Learn Optimizations Techniques in single variables problems.
• CO3: Learn unconstrained Optimizations Techniques in single variables problems
• CO4: Learn constrained optimization techniques and Kuhn-Tucker conditions

CO – PO Mapping