Convex function and optimization techniques

Abstract

Optimization is the process of maximizing or minimizing a desired objective function while satisfying the prevailing constraints. The optimization problems have two major divisions. One is linear programming problem and other is non-linear programming problem. But the modern game theory, dynamic programming problem, integer programming problem also part of the Optimization theory having wide range of application in modern science, economics and management. In the present work I tried to compare the solution of Mathematical programming problem by Graphical solution method and others as well as its theoretic descriptions. As we know that not like linear programming problem where multidimensional problems have a great deal of applications, non-linear programming problem mostly considered only in two variables. Therefore for nonlinear programming problems we have an opportunity to plot the graph in two dimensions and get a concrete graph of the solution space which will be a step ahead in its solutions.
Nonlinear programming deals with the problem of optimizing an objective function in the presence of equality and inequality constraints. The development of highly efficient and robust algorithms and software for linear programming, the advent of high speed computers, and the education of managers and practitioners in regard to the advantages and profitability of mathematical modeling and analysis, have made linear programming an important tool for solving problems in diverse fields. However, many realistic problems cannot be adequately represented or approximated as a linear program owing to the nature of the nonlinearity of the objective function or the nonlinearity of any of the constraints.