A Penalty-free Method For Nonlinear Equality Constrained Optimization

For constrained optimization problem, common methods use penalty parameters. Theoretically, penalty parameters big enough ensure the convergence of the algorithm. However, they often lead to overflow so that the computation fails. Fletcher(1996) first introduced filter methods,which many authors lay emphysis on. In recent years, some research and progresses in this field have been made. Penalty-free method is a class of new algorithms, M.Ulbrich has investigated the case that the gradients of the constraints are linear independent. Being motivated mainly by this, our work generalizes and modifies the approach for linear denpendent assumption on the gradients of the constraints. We analyse a class of penalty-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems in this paper. Without the linear independent assumption on the gradients of the constraints, the algorithmic framework yields global convergence and allows nonmonotonicity independently for both the constraint violation and the value of the Lagrangian function. Finally, some numerical results show that the method presented here is effective.