A filter sequential adaptive cubic regularisation algorithm for nonlinear constrained optimization

Abstract

In this paper, we propose a filter sequential adaptive regularisation algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with linearized constraints is considered to obtain a trial step in each iteration. Composite step methods and reduced Hessian methods are employed to tackle the linearized constraints. As a result, a trial step is decomposed into the sum of a normal step and a tangential step which is computed by a standard ARC subproblem. Then, the new iteration is determined by filter methods and ARC framework. The global convergence of the algorithm is proved under some reasonable assumptions. Preliminary numerical experiments are reported.