A non-iterative method for optimizing linear functions in convex linearly constrained spaces

TL;DR

This paper presents a non-iterative method for solving linear optimization problems in convex, linearly constrained spaces by directly identifying the optimal vertex through constraint bounding conditions.

Contribution

The proposed approach offers a non-iterative alternative to classical linear programming algorithms, utilizing constraint bounding conditions to directly compute the optimal solution.

Findings

Comparable complexity to Simplex method

Non-iterative solution process

Efficient matrix inversion approach

Abstract

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is located at the intersection of the constraints defining the extreme vertex. By identifying the constraints that limit the growth of the objective function value, we formulate linear equations system leading to the optimization problem's solution.The most complex operation of the algorithm is the inversion of a matrix sized by the number of dimensions of the problem. Therefore, the algorithm's complexity is comparable to the corresponding to the classical Simplex method and the more recently developed Linear Programming algorithms. However, the algorithm offers the advantage of being non-iterative.