A two-stage feasible directions algorithm for nonlinear constrained optimization

We present a feasible directions algorithm, based on Lagrangian concepts, for the solution of the nonlinear programming problem with equality and inequality constraints. At each iteration a descent direction is defined; by modifying it, we obtain a feasible descent direction. The line search procedure assures the global convergence of the method and the feasibility of all the iterates. We prove the global convergence of the algorithm and apply it to the solution of some test problems. Although the present version of the algorithm does not include any second-order information, like quasi-Newton methods, these numerical results exhibit a behavior comparable to that of the best methods known at present for nonlinear programming. Research performed while the author was on a two years appointment at INRIA, Rocquencourt, France, and partially supported by the Brazilian Research Council (CNPq).