TY - GEN A1 - Powell, Gary A1 - Weiser, Martin T1 - Container Adaptors N2 - The C++ standard template library has many useful containers for data. The standard library includes two adpators, queue, and stack. The authors have extended this model along the lines of relational database semantics. Sometimes the analogy is striking, and we will point it out occasionally. An adaptor allows the standard algorithms to be used on a subset or modification of the data without having to copy the data elements into a new container. The authors provide many useful adaptors which can be used together to produce interesting views of data in a container. T3 - ZIB-Report - SC-99-41 KW - C++ KW - STL KW - views Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4308 ER - TY - GEN A1 - Volkwein, Stefan A1 - Weiser, Martin T1 - Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods N2 - An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solves. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation. T3 - ZIB-Report - 00-56 KW - nonlinear programming KW - multiplier methods KW - affine invariant norms KW - Burgers' equation Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6243 ER - TY - JOUR A1 - Powell, Gary A1 - Weiser, Martin T1 - Views, A new form of container adaptors JF - C/C++ Users Journal N2 - The C++ standard template library has many useful containers for data. The standard library includes two adpators, queue, and stack. The authors have extended this model along the lines of relational database semantics. Sometimes the analogy is striking, and we will point it out occasionally. An adaptor allows the standard algorithms to be used on a subset or modification of the data without having to copy the data elements into a new container. The authors provide many useful adaptors which can be used together to produce interesting views of data in a container. Y1 - 2000 VL - 18 IS - 4 SP - 40 EP - 51 ER - TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter T1 - The Central Path towards the Numerical Solution of Optimal Control Problems N2 - A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem. T3 - ZIB-Report - 01-12 KW - optimal control KW - interior point methods KW - affine invariance Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6380 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Weiser, Martin T1 - Affine Invariant Adaptive Newton Codes for Discretized PDEs N2 - The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs. T3 - ZIB-Report - 02-33 KW - Affine invariant Newton methods KW - global Newton methods KW - inexact Newton methods KW - adaptive trust region methods KW - nonlinear partial differential equa Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7005 ER - TY - JOUR A1 - Volkwein, S. A1 - Weiser, Martin T1 - Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian SQP Methods JF - SIAM J. Control Optim. Y1 - 2002 VL - 41 IS - 3 SP - 875 EP - 899 ER - TY - GEN A1 - Weiser, Martin T1 - Interior Point Methods in Function Space N2 - A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established. T3 - ZIB-Report - 03-35 KW - interior point methods in function space KW - optimal control KW - complementarity functions Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7578 ER - TY - GEN A1 - Weiser, Martin A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Asymptotic Mesh Independence of Newton's Method Revisited N2 - The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems. T3 - ZIB-Report - 03-13 KW - mesh independence KW - nonlinear partial differential equations KW - Newton method KW - finite element method KW - collocation method Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7352 ER - TY - GEN A1 - Weiser, Martin A1 - Schiela, Anton T1 - Function space interior point methods for PDE constrained optimization N2 - 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. T3 - ZIB-Report - 04-27 KW - interior point methods in function space KW - optimal control KW - complementarity functions Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8027 ER - TY - GEN A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi A1 - Weiser, Martin T1 - The convergence of an interior point method for an elliptic control problem with mixed control-state constraints N2 - The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples. T3 - ZIB-Report - 04-47 KW - interior point methods in function space KW - optimal control KW - mixed control-state constraints KW - Lavrentiev regularization Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8223 ER -