Equivalência entre dois algoritmos de pontos interiores FDIPA e FDA-NCP

Abstract

In this work we present the algorithm of internal points and viable directions denominated FDIPA to solve optimization problems defined by a differentiable function and by inequalities restrictions. The algorithm generates a sequence of interior points from a given interior starting point and converges globally with superlinear order to a Karush-Kuhn-Tucker pair of the problem. At each iteration a descent direction of the potential function is calculated initially by the solution of a system in the dual and primal variables. We also present the FDA algorithm to solve complementarity problems defined by a non-linear differentiable function. We show the equivalence between the two methods in the sense that they generate the same descent, feasible and restoring directions from an update to the Lagrange multipliers of the optimization problem. We perform a comparison between the two methods in a collection of complementarity problems.