OPTIMIZATION

Optimization

Abstract

Optimization is finding the alternative which is the most cost effective or has the highest performance which can be achieved through the functions of minima and maxima, under the particular given constraints, by minimizing the undesired factors and maximizing the desired ones. This paper discuss about various concepts related to optimization and its application on various fields.

Table of Contents

Introduction 2

Optimization in mathematics2

Application in Economics and Finance2

History and Application3

Discussion3

Extrema (Maxima, Minima)3

Global Maximum and Minimum Point4

Discrete Optimization4

Optimization Problem5

Conclusion5

Optimization

Introduction

Optimization in mathematics

Optimization in mathematics, empirical sciences, statistics, management science, computer science with regard to some criteria is the selection of the best element from a set of some alternatives which are available. In the simplest of case, a problem of optimization would consist of a minimizing or maximizing a real function by methodically choosing from within an allowed set input values and in the end computing the value of that function. More generally, in a defined domain, optimization includes the finding of the values which are best available in some objective function (Barrow, 2009).

Application in Economics and Finance

There are a number of optimization questions which arises in the finance and economics domain, which includes the choice of the optimum state of the economy by the society which is also referred as the social choice problem. In economics, optimization improves and extends the usual techniques in optimization, in such a form that it may be adopted for representing and modeling the social choice problems (Intriligator, 1971). Other problems that in the domain of economics include when the optimum level is reached, when it tends to get unique, invent and quasimax which is some associated mathematical concepts, concave or convex conventional relaxation, models of multi objective optimal control and some related programs and computational methods. These methods and techniques are applied to the economic growth models. Simply put, in economics optimization relates to the best use of the available resources in a way which produces maximum level of satisfaction and in other words we can categorize it as the maximum level of output and a minimum usage of the resources (Barrow, 2009).

History and Application

As a mathematical discipline optimization basically concerns with finding the maxima and minima of functions which are subject to the constraints (Intriligator, 1971). The concept of optimization came in the 1940s when t was use dot generate programs for military applications and since then this linear programming technique has been used on a wide variety of problems which included yielding management in airlines to scheduling the product6ion facilities. And today its application ranges to a wide variety of techniques from artificial intelligence, to operations research, to computer science, and most importantly practically almost in all industries to improve the business process (Menezes et al, 2004).

Discussion

Extrema (Maxima, Minima)

In mathematics, extrema which separately is known as the minimum and maximum of a function are the smallest and the largest value that within a given neighborhood the function takes at a point. In more general terms, maxima and minima are basically the least and the greatest ...