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Scenario tree modelling for multistage stochastic programs

Heitsch, Holger; Römisch, Werner

An important issue for solving multistage stochastic programs consists in the approximate representation of the (multivariate) stochastic input process in the form of a scenario tree. In this paper, forward and backward ...

Local Error Estimates for Moderately Smooth ODEs and DAEs

Sickenberger, Thorsten; Weinmüller, Ewa; Winkler, Renate

We discuss an error estimation procedure for the local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index 1 differential-algebraic equations (DAEs). The ...

Discretization-Optimization Methods for Nonlinear Elliptic Optimal Control Problems with State Constraints

Chryssoverghi, Ion; Geiser, Jürgen; Al-Hawasy, J.

We consider an optimal control problem described by a second order elliptic boundary value problem, jointly nonlinear in the state and control, with control and state constraints, where the state constraints and cost ...

Discretization methods with analytical solutions for a convection-diffusion-dispersion-reaction-equation and applications in 2D and 3D for waste-scenarios

Geiser, Jürgen

In this part we describe the numerical methods and the results for our discretization methods for system of convection-diffusiondispersion-reaction equation. The motivation came for the simulation of a scenario of a ...

Discretization-Optimization Methods for Nonlinear Parabolic Relaxed Optimal Control Problems with State Constraints

Chryssoverghi, Ion; Coletsos, J.; Geiser, Jürgen; Kokkinis, B.

We consider an optimal control problem described by a semilinear parabolic partial differential equation, with control and state constraints, where the state constraints and cost involve also the state gradient. Since this ...

Mixed discretisation methods for the Discontinuous Galerkin method with analytical test-functions

Geiser, Jürgen

The idea to this paper is a framework for modifying a standard Discontinuous Galerkin method for convection-diffusion-reaction-equations. We develop an abstract theory for the stability and error-estimates in $L^2$-norms ...

Discretization-Optimization Methods for Nonlinear Elliptic Relaxed Optimal Control Problems with State Constraints.

Chryssoverghi, Ion; Coletsos, J.; Geiser, Jürgen; Kokkinis, B.

We consider an optimal control problem described by a second order elliptic boundary value problem, jointly nonlinear in the state and control with high monotone nonlinearity in the state, with control and state constraints, ...

Mean-square convergence of stochastic multi-step methods with variable step-size

Sickenberger, Thorsten

We study mean-square consistency, stability in the mean-square sense and mean-square convergence of drift-implicit linear multi-step methods with variable step-size for the approximation of the solution of Ito stochastic ...

Picard-Einstein Metrics and Class Fields Connected with Apollonius Cycle

Holzapfel, Rolf-Peter

We define Picard_Einstein metrics on complex algebraic surfaces as Kähler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along ...

On double one-parametric optimization problems and some applications

This paper deals with a special class of quadratic optimization problems with quadratic constraints, which we call double parametric. We try to solve these problems using Pathfollowing Methods with a special case of the ...

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