The dual face algorithm for linear programming (LP) was proposed by the author in 2014. Using QR factorization, it proceeds from dual face to dual face, until reaching an optimal dual face along with dual and primal optimal solutions, unless detecting infeasibility of the problem. On the other hand, a variant of the algorithm using … Read more
The unique feature of the face algorithm \cite{pan14} is that it moves from face to face, rather than from vertex to vertex as the simplex algorithm. It uses the orthogonal projection of the negative objective gradient on the related null space as its search direction. Nevertheless, the algorithm is based on QR factorization, which would … Read more
An attractive feature of the face method \cite{pan14} for solving LP problems is that it uses the orthogonal projection of the negative objective gradient on the related null space as the search direction. However, the method would not be amenable for solving large sparse problems, since it handles the involved normal system by orthogonal transformations. … Read more