JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Generalized Penalty Methods for a Class of Convex Optimization Problems with Pointwise Inequality Constraints

We consider infinite-dimensional convex minimization problems with pointwise inequality constraints. We do not impose a constraint qualification condition, so that first-order necessary conditions are not available. To handle such problems we propose a method which combines advantages both from well-known penalty and barrier methods. For solving the resulting subproblems we develop a Newton-type algorithm in function space and prove its global and locally superlinear convergence. We demonstrate our results by means of an minimization problem subject to a elliptic partial differential equation and pointwise control, zeroand first-order state constraints. Numerical results are presented.