An interior point technique for nonlinear optimization

Projet MODULEFWe propose an approach for the minimization of a smooth function under smooth equality and inequality constraints by interior points algorithms. It consists on the iterative solution, in the primal and dual variables, of Karush-Kuhn-Tucker first order optimality conditions. Based on this approach, different order algorithms can be obtained. To introduce the method, in a first stage we consider the inequality constrained problem and present a globally convergent basic algorithm. Particular first order and quasi-Newton versions of the algorithm are also stated. In a second stage, the general problem is consider and a basic algorithm obtained. This method is simple to code, since it does not involve the solution of quadratic programs but merely that of linear systems of equations. Several applications show that it is also strong and efficient