In this paper we present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a feasibility phase, which reduces a measure of infeasibility, and an optimality phase, which reduces the objective function in a tangential approximation of the feasible set. These two phases are totally independent, and the only coupling between them is provided by the filter. The method is independent of the internal algorithms used in each iteration, as long as these algorithms satisfy reasonable assumptions on their efficiency. Under standard hypotheses, we show two results: for a filter with minimum size, the algorithm generates a stationary accumulation point; for a slightly larger filter, all accumulation points are stationary.

This paper concentrates on the solution of the nonlinear Optimal Power Flow. We describe an interior-point algorithm for nonlinear programming which is an extension of interior-point methods for linear and quadratic programming. Our majot contribution is the inclusion of a mritfuncfion, which is used to measure, at each iteration, the progress along a search direction. Ensuring that the search directions are good descent directions for the merit function provides global convergence for the algorithm.We describe two kinds of merit functions: a classical approach based on a penalty function and a penalty parameter which has to be updated, and a new merit function with no penalties. Numerical tests for a set nf power networks are made to compare the performances of the new merit function and the penalized function with two different parameter updating strategies.