Optimization methods and Quadratic Programming

Abstract

Optimization is the process of maximizing or minimizing the objective function which satisfies the given constraints. There are two types of optimization problem linear and nonlinear. Linear optimization problem has wide range of applications, but all realistic problem cannot be modeled as linear program, so here non-linear programming gains its importance. In the present work I have tried to find the solution of non-linear programming Quadratic problem under different conditions such as when constraints are not present and when constraints are present in the form of equality and inequality sign. Graphical method is also highly efficient in solving problems in two dimensions. Wolfe’s modified simplex method helps in solving the Quadratic programming problem by converting the quadratic problem in successive stages to linear programming which can be solved easily by applying two – phase simplex method. A variety of problems arising in the area of engineering, management etc. are modeled as optimization problem thus making optimization an important branch of modern applied mathematics.