A filter sequential adaptive cubic regularisation algorithm for nonlinear constrained optimization

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. study a generalization of ARC to solve equality constrained optimization by embedding filter technic in ARC framework. Inspired by sequential quadratic programming (SQP) methods to handle constrained optimization, we construct a filter sequential ARC algorithm. In each iteration, composite step approaches are employed to compute the trial step which is decomposed into the sum of the normal step and the tangential step. The normal step is used to reduce the constraint violation degree, and it is required to satisfy the linearization constraint. The tangential step is used to provide sufficient reduction of the model. It is computed by solving a standard ARC subproblem which is constructed via reduced Hessian methods. After the trial step is computed, an acceptance mechanism by using filter method is used to decide whether the step is accepted. Global convergence is proved under some suitable assumptions.