One vs.Two vs. Multidimensional Searches for Optimization Methods

Abstract

Optimization is an important tool for decision makers to make better and more informed decisions. Most algorithms designed to solve optimization models are considered one-dimensional search methods. That is, an improved solution is obtained at each iteration by moving along a single search direction and solving a one-dimensional subproblem. In contrast, multidimensional search methods consider more than one search direction and solve a multidimensional subproblem at each step. This article presents an extensive review of existing multidimensional search algorithms to solve optimization problems. The article also describes a modified and improved version of the slope algorithm, a technique to perform multidimensional searches. This version aims to improve the numerical stability of the slope algorithm. Some computational experiments show that the modified version is still effective and more reliable.