Contributed Session Mon.1.H 0112

Monday, 10:30 - 12:00 h, Room: H 0112

Cluster 16: Nonlinear programming [...]

Algorithms for optimal control I

 

Chair: Dennis Janka

 

 

Monday, 10:30 - 10:55 h, Room: H 0112, Talk 1

Dennis Janka
Separable formulations of optimum experimental design problems

Coauthors: Hans-Georg Bock, Stefan Körkel, Sebastian Sager

 

Abstract:
We consider optimal control problems coming from nonlinear optimum experimental design. These problems are non-standard in the sense that the objective function is not of Bolza type. In a straightforward direct solution approach one discretizes the controls and regards the states as dependent variables. However, this often leads to poor convergence properties of the resulting NLP.
We propose a reformulation of the problem to a standard optimal control problem by introducing additional variables. It is then possible to attack this problem with direct state-of-the-art methods for optimal control with better convergence properties, e.g., multiple shooting. The reformulation gives rise to a highly structured NLP due to the multiple shooting discretization as well as due to the peculiarities of the optimum experimental design problem.
We highlight some of these structures in the constraints, the objective function, and the Hessian matrix of the Lagrangian, and present ways to exploit them leading to efficient SQP methods tailored to optimum experimental design problems. Numerical results are presented comparing the new separable formulations to an existing implementation.

 

 

Monday, 11:00 - 11:25 h, Room: H 0112, Talk 2

Kathrin Hatz
Hierarchical dynamic optimization - Numerical methods and computational results for estimating parameters in optimal control problems

Coauthors: Hans-Georg Bock, Johannes P. Schlöder

 

Abstract:
We are interested in numerical methods for hierarchical dynamic optimization problems with a least-squares objective on the upper level and a optimal control problem (OCP) with mixed path-control constraints on the lower level. The OCP can be considered as a model (a so-called optimal control model) that describes optimal processes in nature, such as the gait of cerebral palsy patients. The optimal control model includes unknown parameters that have to be determined from measurements.
We present an efficient direct all-at once approach for solving this class of problems. The main idea is to discretize the infinite dimensional bilevel problem, replace the lower level nonlinear program (NLP) by its first order necessary conditions (KKT conditions), and solve the resulting complex NLP with a tailored sequential quadratic programming (SQP) method. The performance of our method is discussed and compared with the one of alternative approaches. Furthermore, we present an optimal control model for a cerebral palsy patient which has been identified from real-world motion capture data that has been provided by the Motion Laboratory of the University Hospital Heidelberg.

 

 

Monday, 11:30 - 11:55 h, Room: H 0112, Talk 3

Carsten Gräser
Truncated nonsmooth newton multigrid methods for nonsmooth minimization

 

Abstract:
The combination of well-known primal-dual active-set methods for
quadratic obstacle problems with linear multigrid solvers leads
to algorithms that sometimes converge very fast, but fail to
converge in general. In contrast nonlinear multilevel relaxation
converges globally but exhibits suboptimal convergence speed and
complexity.
Combining nonlinear relaxation and active-set ideas we derive the
globally convergent "truncated nonsmooth Newton multigrid''
(TNNMG) method. While its complexity is comparable to linear
multigrid its convergences in general much faster than multilevel
relaxation. Combined with nested iteration it turns out to be
essentially as fast as multigrid for related linear
problems. This the method relies on minimization the
generalization to more other nonquadratic, nonsmooth energies is
straight forward.

 

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