CONICET | Buscador de Institutos y Recursos Humanos

The Feasible Arc Interior Point Algorithm (FAIPA) is a non linear optimization method which defines, at each iteration, the search path by composing three basic directions. For this, a system of linear algebraic equations should be solved for each component. This three linear systems presents the following characteristics: - They have all the same matrix, and the right hand side vector is different for each one.- By performing a change in the variables these systems are symmetric.- The size of the system is the number of design variables plus the total number of constraints (both equality and inequality constraints).A factorization of the type LDU (with U transpose of L) is proposed. The number of operations required in this factorization is two thirds the size of the matrix to a power three and it should be performed once at each iteration. Besides backward/forward substitutions are to be performed for each of the three systems, amounting some operations as the square of the matrix size. The time complexity for these operations is great for great systems. In this paper a block LDU factorization is proposed for this problem. By this way a set of uncoupled triangular systems are obtained, which allows to perform a parallel solving for this process stage.