# OPTIMIZATION TECHNIQUES

OBJECTIVE: On completion of this course,the students will be able to solve nonlinear programming,games,sequencing and replacement problems.

## 1.CALCULUS OF VARIATIONS

Extrema of functions of several variables with and without constraints - functionals - Euler's equation for general cases - variational problems in parametric form - Natural boundary conditions.

## 2.NON-LINEAR PROGRAMMING –I

Basic ideas of one dimensional and multidimensional optimization problems - Unconstrained and constrained problems - Lagrange's multipliers - Kuhn-Tucker's conditions - Quadratic programming - Wolf's method - Beale's method.

## 3.NON-LINEAR PROGRAMMING- II

Unconstrained optimization techniques - Direct search methods - Powell's method - Hooke and Jeeves method - Rosenbrock's method - Decent methods - steepest descent method - Conjugate gradient method.

## 4.GAME THEORY

Two person Zero - sum games - Maximin minimax principle - Saddle point - solution by dominance property - graphical solution of 2xn and mx2 games - solution of game by L.P.P. methods - Brown's iterative method.

## 5.SEQUENCING AND REPLACEMENT PROBLEMS

Sequencing problem - problems with n-jobs and two machines - problems with n-jobs and three machines - replacement of items that deteriorate with time without and with money value changed - Individual replacement policy - Group replacement problem.