Showing papers by "Andrea Walther published in 2010"

New Algorithms for Optimal Online Checkpointing

Abstract: Frequently, the computation of derivatives for optimizing time-dependent problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution may be required. Similar information is needed in the context of a posteriori error estimation with respect to a given functional. In the area of flow control, especially for three dimensional problems, it is usually impossible to keep track of the full forward solution due to the lack of storage capacities. Further, for many problems, adaptive time-stepping procedures are needed toward efficient integration schemes in time. Therefore, standard optimal offline checkpointing strategies are usually not well suited in that framework. In this paper we present two algorithms for an online checkpointing procedure that determines the checkpoint distribution on the fly. We prove that these approaches yield checkpointing distributions that are either optimal or almost optimal with only a small gap to optimality. Numerical results underline the theoretical results.

An adjoint-based SQP algorithm with quasi-Newton Jacobian updates for inequality constrained optimization

Abstract: We present a sequential quadratic programming (SQP) type algorithm, based on quasi-Newton approximations of Hessian and Jacobian matrices, which is suitable for the solution of general nonlinear programming problems involving equality and inequality constraints. In contrast to most existing SQP methods, no evaluation of the exact constraint Jacobian matrix needs to be performed. Instead, in each SQP iteration only one evaluation of the constraint residuals and two evaluations of the gradient of the Lagrangian function are necessary, the latter of which can efficiently be performed by the reverse mode of automatic differentiation. Factorizations of the Hessian and of the constraint Jacobian are approximated by the recently proposed STR1 update procedure. Inequality constraints are treated by solving within each SQP iteration a quadratic program (QP), the dimension of which equals the number of degrees of freedom. A recently proposed gradient modification in these QPs takes account of Jacobian inexactness in the active set determination. Superlinear convergence of the procedure is shown under mild conditions. The convergence behaviour of the algorithm is analysed using several problems from the Hock-Schittkowski test library. Furthermore, we present numerical results for an optimization problem based on a small periodic adsorption process, where the Jacobian of the equality constraints is dense.

An Inexact Trust-Region Algorithm for the Optimization of Periodic Adsorption Processes

Abstract: Periodic adsorption processes have gained increasing commercial importance as an energy-efficient separation technique over the past two decades. Based on fluid-solid interactions, these systems never reach steady state. Instead they operate at cyclic steady state, where the bed conditions at the beginning of the cycle match with those at the end of the cycle. Nevertheless, optimization of these processes remains particularly challenging, because cyclic operation leads to dense Jacobians, whose computation dominates the overall cost of the optimization strategy. To efficiently handle these Jacobians during optimization and reduce the computation time, this work presents a new composite step trust-region algorithm for the solution of minimization problems with both nonlinear equality and inequality constraints, and combines two approaches developed in Walther 1 and Arora and Biegler. 2 Instead of forming and factoring the dense constraint Jacobian, this algorithm approximates the Jacobian of equality constraints with a specialized quasi-Newton method. Hence it is well suited to solve optimization problems related to periodic adsorption processes. In addition to allowing inexactness of the Jacobian and its null-space representation, the algorithm also provides exact second-order information in the form of Hessian—vector products to improve the convergence rate. The resulting approach' also combines automatic differentiation and more sophisticated integration algorithms to evaluate the direct sensitivity and adjoint sensitivity equations. A 5-fold reduction in computation is demonstrated with this approach for two periodic adsorption optimization problems: a simulated moving bed system and a nonisothermal vacuum swing adsorption O 2 bulk gas separation.

Three-dimensional reconstruction of a comet nucleus by optimal control of Maxwell's equations: A contribution to the experiment CONSERT onboard space craft Rosetta

Abstract: COmet Nucleus Sounding Experiment by Radio Wave Transmission (CONSERT) is one of 20 experiments onboard the ESA mission Rosetta and aimed at the reconstruction of the unknown internal material parameter distribution of a comet nucleus The details on the experiment setup can be found in [1], [2] CONSERT consists of a lander module which attaches to the surface of the comet and an orbiter module which circulates the comet in space An electromagnetic sounding of the comet nucleus will be achieved by a signal link between the lander and orbiter antenna system We propose an optimal control approach to solve for the unknown 3D material parameter distribution of the comet nucleus We optimize the computed electromagnetic field distribution at the receiver locations for the measured (observed) electromagnetic field distribution by controlling the material parameters The target functional, the difference between computed and observed field for all receiver locations and time steps is minimized by means of a gradient-based quasi-Newton optimization algorithm The optimal control problem is solved if the target functional yields its global minimum

Algorithmic Differentiation for Calculus‐based Optimization

Abstract: For numerous applications, the computation and provision of exact derivative information plays an important role for optimizing the considered system but quite often also for its simulation. This presentation introduces the technique of Algorithmic Differentiation (AD), a method to compute derivatives of arbitrary order within working precision. Quite often an additional structure exploitation is indispensable for a successful coupling of these derivatives with state‐of‐the‐art optimization algorithms. The talk will discuss two important situations where the problem‐inherent structure allows a calculus‐based optimization. Examples from aerodynamics and nano optics illustrate these advanced optimization approaches.