We consider the inequality constrained nonlinear programming problem and an SQP algorithm for its solution. We are primarily concerned with two aspects of the general procedure, namely, the approximate solution of the quadratic program, and the need for an appropriate merit function. We first describe an (iterative) interior-point method for the quadratic programming subproblem that, no matter when it its terminated, yields a descent direction for a suggested new merit function. An algorithm based on ideas from trust-region and truncated Newton methods, is suggested and some of our preliminary numerical results are discussed. '.?«1