Numerical and Engineering Optimization Methods Tuition

Syllabus May Vary As Per University Curriculum

• Numerical techniques: Root finding in one dimension, bisection method, Newton-Raphson method and regula-falsi method, solution of ordinary differential equations, multistep method, Runge-Kutta method with fixed step size and variable step size

• Linear programming –formulation-Graphical and simplex methods[1]Big-M Method-Two phase method-Dual simplex method-Primal Dual problems

• Unconstrained one-dimensional optimization techniques -Necessary and sufficient conditions –Unrestricted search methods-Fibonacci and golden section method-Quadratic Interpolation methods, cubic interpolation

• Unconstrained n dimensional optimization techniques – direct search methods –Random search –pattern search and Rosenbrock’s hill claiming method- Descent Methods-Steepest descent, conjugate gradient, quasi -Newton method

• Constrained optimization Techniques- Necessary and sufficient conditions –Equality and inequality constraints-Kuhn-Tucker Conditions-Gradient projection method-cutting plane method[1]penalty function method

Text Book:

[1] Rao, S.S.,‟Optimization :Theory and Application‟ Wiley Eastern Press, 2nd Ed

[2] Taha, H.A., Operations Research –An Introduction, Prentice Hall of India

[3] Fox, R.L., Optimization methods for Engineering Design‟, Addition Welsey