2,236 research outputs found
Optimal control of Allen-Cahn systems
Optimization problems governed by Allen-Cahn systems including elastic
effects are formulated and first-order necessary optimality conditions are
presented. Smooth as well as obstacle potentials are considered, where the
latter leads to an MPEC. Numerically, for smooth potential the problem is
solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an
obstacle potential first numerical results are presented
Towards a Lagrange-Newton approach for PDE constrained shape optimization
The novel Riemannian view on shape optimization developed in [Schulz, FoCM,
2014] is extended to a Lagrange-Newton approach for PDE constrained shape
optimization problems. The extension is based on optimization on Riemannian
vector space bundles and exemplified for a simple numerical example.Comment: 16 pages, 4 figures, 1 tabl
Applications of inverse simulation to a nonlinear model of an underwater vehicle
Inverse simulation provides an important alternative
to conventional simulation and to more formal
mathematical techniques of model inversion. The
application of inverse simulation methods to a nonlinear
dynamic model of an unmanned underwater vehicle with
actuator limits is found to give rise to a number of
challenging problems. It is shown that this particular
problem requires, in common with other applications that
include hard nonlinearities in the model or discontinuities
in the required trajectory, can best be approached using a
search-based optimization algorithm for inverse
simulation in place of the more conventional Newton-
Raphson approach. Results show that meaningful inverse
simulation results can be obtained but that multi-solution
responses exist. Although the inverse solutions are not
unique they are shown to generate the required
trajectories when tested using conventional forward
simulation methods
Dynamic Congestion and Tolls with Mobile Source Emission
This paper proposes a dynamic congestion pricing model that takes into
account mobile source emissions. We consider a tollable vehicular network where
the users selfishly minimize their own travel costs, including travel time,
early/late arrival penalties and tolls. On top of that, we assume that part of
the network can be tolled by a central authority, whose objective is to
minimize both total travel costs of road users and total emission on a
network-wide level. The model is formulated as a mathematical program with
equilibrium constraints (MPEC) problem and then reformulated as a mathematical
program with complementarity constraints (MPCC). The MPCC is solved using a
quadratic penalty-based gradient projection algorithm. A numerical study on a
toy network illustrates the effectiveness of the tolling strategy and reveals a
Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the
Proceedings of the 20th International Symposium on Transportation and Traffic
Theory, 2013, the Netherland
- …