**DESCRIPTION OF COURSES**

**AS 606 OPTIMIZATION TECHNIQUES (1L+1P) I**

**Objective**

This course is meant for exposing the students to the mathematical details of the techniques for obtaining optimum solutions under constraints for desired output. They will be taught numerical methods of optimization, linear programming techniques, nonlinear programming and multiple objective programming. Students will also be exposed to practical applications of these techniques.

**Theory**

UNIT I

Classical and numerical methods of optimization: constrained optimization, Lagrange multipliers, necessary conditions for an extremum. Statistical applications. Optimization and inequalities. Classical inequalities, like Cauchy-Schwarz Inequality, Jensen Inequality and Markov Inequality.

UNIT II

Numerical evaluation of roots of equations. Sequential search methods - Fibonacci search method. Random search method: method of Hooke and Jeeves, simplex search method. Gradient methods, like Newton’s method and method of steepest ascent.

UNIT III

Linear programming techniques, simplex method, Karmarkar’s algorithm, duality and sensitivity analysis, zero-sum two-person finite games and linear programming. Integer programming. Statistical applications.

UNIT IV

Nonlinear programming, Kuhn-Tucker sufficient conditions. Elements of multiple objective programming, dynamic programming. Optimal control theory: Pontryagin’s maximum principle, time-optimal control problems. Quadratic programming.

**Practicals**

Problems based on classical optimization techniques, optimization techniques with constraints, minimization problems using numerical methods. Linear programming (LP) problems through graphical method, simplex method, simplex two-phase method, primal and dual method. Sensitivity analysis for LP problem, LP problem using Karmarkar’s method. Problems based on Quadratic programming, integer programming, dynamic programming. Problems based on Pontryagin’s maximum principle.

**Suggeste****d Readings**

- Rao, S.S. 2007.
*Engineering Optimization: Theory and Practice*. New Age International Publishers. - Rustagi, J.S. 1994.
*Optimization Techniques in Statistics*. Academic Press. - Taha, H.A. 2007.
*Operations Research: Introduction with CD*. Pearson Education. - Zeleny, M. 1974.
*Linear Multiobjective Programming*. Springer.