The Optimum of a Quadratic Univariate Response Function Is Located at the Origin

Idorenyin Etukudo

doi:10.4236/ajor.2017.76024

Abstract

This work has successfully shown that the optimum of a quadratic response function with zero coefficients except that of the quadratic term lies at the origin. This was achieved by using optimal designs technique for solving unconstrained optimization problems with quadratic surfaces. In just one move, the objective of the work, that is, xmin = 0 was realized.

Highlights

Open AccessThis paper seeks to show that given a quadratic univariate response function with zero coefficients except that of the quadratic term, the optimum lies at the origin. [1] and [2] stated that even though very few problems exist in real life where managers are concerned with taking decisions involving only one decision variable, this kind of study is justified since it forms the basis of simple extensions which plays a cardinal role to the development of a general multivariate algorithm.Traditional solution techniques for solving unconstrained optimization problems with single variable abound
This work has successfully shown that the optimum of a quadratic response function with zero coefficients except that of the quadratic term lies at the origin
This was achieved by using optimal designs technique for solving unconstrained optimization problems with quadratic surfaces

Summary

Introduction

This paper seeks to show that given a quadratic univariate response function with zero coefficients except that of the quadratic term, the optimum lies at the origin. [1] and [2] stated that even though very few problems exist in real life where managers are concerned with taking decisions involving only one decision variable, this kind of study is justified since it forms the basis of simple extensions which plays a cardinal role to the development of a general multivariate algorithm (see [3]). Traditional solution techniques for solving unconstrained optimization problems with single variable abound. These techniques require many iterations involving very tedious computations [4]. Some of the line search techniques in this group include Fibonacci and Golden Section Search techniques. These techniques identify the interval of uncertainty containing the optimum and seek to minimize this interval, without locating the exact optimum point and the computational efforts in achieving this are enormous. The procedure in Fibonacci Search technique follows a numerical sequence known as Fibonacci numbers as shown by [1]

Etukudo DOI

Etukudo

Numerical Illustration

Conclusion