38,791 research outputs found
Cut time in sub-Riemannian problem on Engel group
The left-invariant sub-Riemannian problem on the Engel group is considered.
The problem gives the nilpotent approximation to generic nonholonomic systems
in four-dimensional space with two-dimensional control, for instance to a
system which describes motion of mobile robot with a trailer. The global
optimality of extremal trajectories is studied via geometric control theory.
The global diffeomorphic structure of the exponential mapping is described. As
a consequence, the cut time is proved to be equal to the first Maxwell time
corresponding to discrete symmetries of the exponential mapping
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
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