Advances in Decision Sciences (ADS)

Optimal Solution Techniques in Decision Sciences A Review

Optimal Solution Techniques in Decision Sciences A Review

Title

Optimal Solution Techniques in Decision Sciences A Review

Authors

Abstract

Methods to find the optimization solution are fundamental and extremely crucial for scientists to program computational software to solve optimization problems efficiently and forpractitioners to use it efficiently. Thus, it is very essential to know about the idea, origin, and
usage of these methods. Although the methods have been used for very long time and the
theory has been developed too long, most, if not all, of the authors who develop the theory
are unknown and the theory has not been stated clearly and systematically. To bridge the
gap in the literature in this area and provide academics and practitioners with an overview
of the methods, this paper reviews and discusses the four most commonly used methods
to find the optimization solution including the bisection, gradient, Newton-Raphson, and
secant methods. We first introduce the origin and idea of the methods and develop all the
necessary theorems to prove the existence and convergence of the estimate for each method.
We then give two examples to illustrate the approaches. Thereafter, we review the literature of the applications of getting the optimization solutions in some important issues and
discuss the advantages and disadvantages of each method. We note that all the theorems
developed in our paper could be well-known but, so far, we have not seen any book or paper
that discusses all the theorems stated in our paper in detail. Thus, we believe the theorems
developed in our paper could still have some contributions to the literature. Our review is
useful for academics and practitioners in finding the optimization solutions in their studies.

Keywords

bisection method, gradient method, Newton-Raphson method, secant method

Classification-JEL

A10, G00, G31, O32

Pages

114-161

https://doi.org/10.47654/v23y2019i1p114-161

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