Geometry on Optimal Problem

Abstract

We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the same time, it ensures that previously fulfilled constraints are not breached during this process. The method is based on geometrical properties of n-dimensional space and can be used on any type of linear constraints (>, =, $\geq$), moreover it can be used when the feasible region is non-full-dimensional.