Showing papers by "Andrea Walther published in 2004"
02 Nov 2004
TL;DR: The more common multi-level checkpointing as well as the less known binomial checkpointing are presented and the checkpointing approaches are compared with respect to the number of time steps the adjoint of which can be calculated, the run-time needed for the adjointed calculation and the memory requirement.
Abstract: Checkpointing techniques become more and necessary for the computation of adjoints. This paper presents the more common multi-level checkpointing as well as the less known binomial checkpointing. The checkpointing approaches are compared with respect to the number of time steps the adjoint of which can be calculated, the run-time needed for the adjoint calculation and the memory requirement. Some examples illustrate the shown results
37 citations
TL;DR: It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem.
Abstract: This paper deals with the numerical solution of optimal control problems for ODEs. The methods considered here rely on some standard optimization code to solve a discretized version of the control problem under consideration. We aim to make available to the optimization software not only the discrete objective functional, but also its gradient. The objective gradient can be computed either from forward (sensitivity) information or backward (adjoint) information. The purpose of this paper is to discuss various ways of adjoint computation. It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem. Particular attention is given to automatic differentiation techniques which generate automatically a suitable integrator.
37 citations
TL;DR: A new search algorithm for determining a reversal schedule that minimizes the runtime of the reversal process for a given number of checkpoints is presented, made to grow only quadratically with the number of time steps to be reverted.
Abstract: The reversal of a program execution can be helpful for several purposes. The reverse mode of automatic differentiation, parameter estimation, and debugging represent some of the tasks that may require the intermediate values of a calculation in reverse order. The recording of a complete execution log forms the simplest approach to providing the data required for the reversal. However, this “store-everything” method causes an enormous demand for memory. The generation of the execution log piece by piece offers the possibility to reduce the storage requirement. To that end the forward calculation is restarted from suitably placed checkpoints leading to a more or less complicated reversal schedule.This paper deals with the reversal of evaluation procedures that consist of a sequence of time steps with varying computational complexity. We present a new search algorithm for determining a reversal schedule that minimizes the runtime of the reversal process for a given number of checkpoints. By exploiting a certain monotonicity property, the search algorithm based on dynamic programming can be made to grow only quadratically with the number of time steps to be reverted. We report the runtime savings that can be achieved performing the reversal with an optimal, i.e. time-minimal, reversal schedule for a test problem based on Burgers’ equation.
7 citations
TL;DR: The structure of such parallel reversal schedules that use the checkpointing technique on a multi-processor machine are described and they are shown to require the least number of processors and memory locations to store checkpoints given a certain number of time steps.
Abstract: For derivative calculations, debugging, and interactive control one may need to reverse the execution of a computer program for given inputs. If any increase of the time needed for the reversal is unacceptable, the availability of enough auxiliary processors provides the possibility to reverse the computer program with minimal temporal complexity and a surprisingly small spatial complexity using parallel reversal schedules. This paper describes the structure of such parallel reversal schedules that use the checkpointing technique on a multi-processor machine. They are shown to require the least number of processors and memory locations to store checkpoints given a certain number of time steps.
6 citations
20 Jun 2004
TL;DR: Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order using ADOL-C or similar automatic differentiation packages.
Abstract: Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order. The successive calculation of Taylor coefficients involves the solution of nonlinear algebraic equations by some variant of the Gauss-Newton method. Hence, one needs to evaluate certain Jacobians and several right hand sides. Without advocating a particular solver we discuss how this information can be efficiently obtained using ADOL-C or similar automatic differentiation packages.
5 citations
01 Jan 2004
TL;DR: This article used quasi-Newton metodos to solve ecuaciones no lineales and problemas de optimizacion de pequena or mediana dimension, e.g., problemas extensos y estructurados.
Abstract: Los metodos quasi-Newton basados en actualizaciones de la secante de bajo rango han sido ampliamente usados por varias decadas para resolver ecuaciones no lineales y problemas de optimizacion de pequena o mediana dimension. La adaptacion de estos metodos a la solucion de problemas extensos y estructurados no ha sido siempre exitosa
2 citations
01 Jan 2004
TL;DR: This article reviews the use of Automatic (or Algorithmic) Differentiation (AD) in nonlinear programming problems arising from the discretization of constrained optimal control problems with ordinary differential equations.
Abstract: This article reviews the use of Automatic (or Algorithmic) Differentiation (AD) in nonlinear programming problems arising from the discretization of constrained optimal control problems with ordinary differential equations Depending on the number and type of constraints, the forward or reverse mode of AD are favoured As an example, we consider a fast turn-around manoeuvre of an industrial robot