A smoothing approach for the optimal parameter selection problem with continuous inequality constraint
In this paper, we consider a class of optimal parameter selection problems with continuous inequality constraints. By introducing a smoothing parameter, we formulate a sequence of KKT (Karush-Kuhn-Tucker) systems of this problem and then transform it into a system of constrained nonlinear equations. Then, the first- and second-order gradients formulae of the cost functional and the constraints are derived. On this basis, a smoothing projected Newton-type algorithm is developed to solving this system of nonlinear equations. To illustrate the effectiveness of the proposed method, some numerical results are solved and presented.
optimal parameter selection problem continuous inequality constraint projected newton-type algorithm kkt system