Duality of the improved algebraic method (DIAM)

In this note we present a variant of the improved algebraic method (IAM) using a duality analysis to solve linear programming (LP) problems where more insights to the method are presented. When the coordinates of all vertices are computed, any feasible point can be expressed as a linear combination of the vertices. The objective function is expressed as a weighted sum of its evaluation at the feasible vertices and the optimal point is associated with the highest/lowest coefficient of the weighted sum.