Improved strategies of the Equality Set Projection (ESP) algorithm for computing polytope projection

Abstract

Abstract. ​​​​​​​This paper proposes an optimization method for the Equality Set Projection algorithm to compute the orthogonal projection of polytopes. However, its computational burden significantly increases for the case of dual degeneracy, which limits the application of the algorithm. Two improvements have been proposed to solve this problem for the Equality Set Projection algorithm: first, a new criterion that does not require a discussion of the uniqueness of the solution in linear programming, which simplifies the algorithm process and reduces the computational cost; and second, an improved method that abandons the calculation of a ridge's equality set to reduce the computational burden in the case of high-dimensional dual degeneracy.