This paper describes an interior point algorithm for solving nonlinear programming problems. The approach we consider here is a classical one. It consists of transforming the original problem into one with only equality constraint, the inequalities being placed into the objective through a logarithmic barrier function. The KKT optimality conditions are solved by the Newton method. The direction of moving is given by a linear algebraic system, which must be solved at each iteration. The step length computation, which is the critical point of the algorithm, is based on a merit function which determines the values of the barrier parameter. This ensures the descendance character of the search direction. The conditions for step length computation include: the boundary of variables, the positivity of the slack and dual variables, the centrality of iterations, the correlation between the speed of decreasing the pure optimality conditions and the transversality conditions, as well as the Wolfe conditions. A crude implementation of the algorithm shows the performance of this approach on a number of nonlinear problems from the Hock-Schittkowski set of problems. Comparisons with a modified penalty-barrier algorithm implemented as a SPENBAR package show that the method is efficient on at least some classes of nonlinear models.
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