A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function (Q939555)

The authors propose an algorithm for the solution of finite-dimensional, nonlinear, smooth, constrained optimization problems. Therefore a sequential quadratically constrained quadratic programming method is presented which differs from standard sequential quadratic programming (SQP) by using quadratic instead of linear constraints for each subproblem. This approach is a simple extension of the SQP theory used for example by \textit{Y.-H. Dai} and \textit{K. Schittkowski} [Pac. J. Optim. 4, No.~2, 335--351 (2008; Zbl 1154.65046)], the algorithm presented here follows this paper in many details. The augmented Lagrange function used as merit function and also the problem formulation is nearly the same, especially after the final extension from inequality constraints to general constraints and to a nonmonotone linesearch -- apart of course from the added quadratic terms which one has to carry along. Convergence rates are proved to be superlinear and quadratic under certain conditions. No numerical results and hence evidence for superiority of the theory are given so far.