Optimization Techniques

1.Linear programming - formulation-Graphical and simplex methods-Big-M methodTwo phase method-Dual simplex method-Primal Dual problems.

2.Unconstrained one dimensional optimization techniques - Necessary and sufficient conditions -Unrestricted search methods-Fibonacci and golden section methodQuadratic Interpolation methods, cubic interpolation and direct root methods.

3. Unconstrained n dimensional optimization techniques - direct search methods - Random search -pattern search and Rosen brooch’s hill claiming methodDescent methods- Steepest descent, conjugate gradient, quasi -Newton method.

4.Constrained optimization Techniques- Necessary and sufficient conditions - Equality and inequality constraints-Kuhn-Tucker conditions-Gradient projection method-cutting plane method- penalty function method .

5.Dynamic programming- principle of optimality- recursive equation approach-application to shortest route, cargo-loading, allocation and production schedule problems.

References :

1. Rao,S.S.,Optimization :Theory and Application Wiley Eastern Press, 2nd edition 1984.

2. Taha,H.A., Operations Research -An Introduction,Prentice Hall of India,2003.

3. Fox, R.L., „Optimization methods for Engineering Design, Addition Welsey, 1971.