Switching stepsize strategies for PDIP

In this chapter we present a primal-dual interior point algorithm for solving constrained nonlinear programming problems. Switching rules are implemented that aim at exploiting the merits and avoiding the drawbacks of three different merit functions. The penalty param-eter is determined using an adaptive penalty strategy that ensures a descent property for the merit function. The descent property is as-sured without requiring positive definiteness of the Hessian used in the subproblem generating search direction. It is also shown that the penalty parameter does not increase indefinitely, dispensing thus with the various numerical problems occurring otherwise. Global conver-gence of the algorithm is achieved through the monotonic decrease of a properly chosen merit function. The algorithm is shown to possess convergent stepsizes, and therefore does not impede superlinear con-vergence under standard assumptions