Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

Interior-Point Methods for PDE-Constrained Optimization

In applied sciences PDEs model an extensive variety of phenomena. Typically the final goal of simulations is a system which is optimal in a certain sense. For instance optimal control problems identify a control to steer a system towards a desired state. Inverse problems seek PDE parameters which are most consistent with measurements. In these optimization problems PDEs appear as equality const...

Primal-dual interior-point methods for PDE-constrained optimization

Abstract. This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L-setting is analyzed, but also a more involved L-analysis, q < ∞, is pr...

Function space interior point methods for PDE constrained optimization

A primal-dual interior point method for optimal control problems with PDE constraints is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed. Numerical results from an inexact continuation method applied to a model problem are shown. AMS MSC 2000: 49M15, 90C48, 90C51

Superlinear convergence of the control reduced interior point method for PDE constrained optimization

A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadrat-ically, if the optim...