New conical internally evolutive linear programming algorithm

Optimality in the range space is expressed as a tangency condition for an affine set and a cone. In a previous paper, an algorithm was introduced that reaches tangency keeping the two sets nonintersecting. Here, we introduce an exact finite-convergence evolutive algorithm that reaches tangency while keeping the two sets intersecting. In the process of developing the algorithm, we add some completion to the theory (e.g., the description of the contact polytope). Furthermore, we introduce a new formula to express the maximum, which is the primal counterpart of the dual formula introduced in a previous paper.