this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can

. We provide an effective and efficient implementation of a sequential quadratic programming (SQP) algorithm for the general large scale nonlinear programming problem. In this algorithm the quadratic programming subproblems are solved by an interior point method that can be prematurely halted by a trust region constraint. Numerous computational enhancements to improve the numerical performance are presented. These include a dynamic procedure for adjusting the merit function parameter and procedures for adjusting the trust region radius. Numerical results and comparisons are presented. Key words: nonlinear programming, interior point, SQP, merit function, trust region, large scale 1. Introduction. In a series of recent papers, [3], [6], and [8], the authors have developed a new algorithmic approach for solving large, nonlinear, constrained optimization problems. This proposed procedure is, in essence, a sequential quadratic programming (SQP) method that uses an interior point algorithm...

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 is 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.

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual ℓ1 linearly constrained Lagrangian (pdℓ1-LCL) method. Key words. Nonlinear programming, nonlinear inequality constraints, augmented Lagrangian methods, bound constrained Lagrangian methods, linearly constrained Lagrangian methods, primal-dual methods.