An algorithm for projecting onto simplicial cones. (2nd October 2020) - Kwon, Oh Kang
Abstract : Many optimization problems that arise in practice can be reduced to the problem of computing the projection of a given vector in a Euclidean space onto the simplicial cone generated by a set of linearly independent vectors. For example, the well-known problem in finance of determining the global minimum variance portfolio with no short sales constraint can be transformed to a problem of this type. Although the projection problem does not admit a solution in closed form, various numerical techniques have been proposed for its solution. This paper introduces a simple and efficient new algorithm for the solution to this problem and compares its performance to other algorithms proposed in the literature. It is shown that the algorithm is very efficient and orders of magnitude faster than methods introduced, for example, in Barrios et al. [Projection onto simplicial cones by Picard's method. Linear Algebra Appl. 2015;480:27–43], and comparable to algorithms in commercial software such as Cplex .