On an inexact trust-region SQP-filter method for constrained nonlinear optimization

A class of trust-region algorithms is developed and analyzed for the solution of optimization problems with nonlinear equality and inequality constraints. Based on composite-step trust region methods and a filter approach, the resulting algorithm also does not require the computation of exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices. As demonstrated on numerical examples, this feature has significant potential benefits for problems where Jacobian calculations are expensive.