Contributed Session Wed.2.H 0112

Wednesday, 13:15 - 14:45 h, Room: H 0112

Cluster 16: Nonlinear programming [...]

Applications of optimization I


Chair: Marc C. Steinbach



Wednesday, 13:15 - 13:40 h, Room: H 0112, Talk 1

Makoto Yamashita
An approach based on shortest path and connectivity consistency for sensor network localization problems

Coauthors: Zih-Cin Lin, I-Lin Wang


Sensor network localization (SNL) problems are considered to be an important topic due to the variety of applications including a molecular conformation. In SNL problems, we have anchors (known locations) and sensors (unknown locations). The distance between a pair of them is available if the pair is closer than the radio range. From this partial distance information, we want to infer the sensor locations.
SDP relaxation approaches often generate high quality solution, but their computation cost can easily grow up for large SNLs. To solve SNLs with a cheaper cost, we combine several heuristics.
We first compute the shortest paths from anchors to sensors hopping some sensors. For each sensor, we use the path lengths to guess its location roughly. After applying a gradient method, we adjust the sensors based on connectivity consistency. When a pair should be closer than the radio range, but the computed distance is longer than it, we ‘pull’ the sensor locations. We repeat the shortest path and the adjustment, until we fix all the sensors as reliable.
Numerical results show that this approach obtains the sensor locations with relatively good accuracy using low computation cost.



Wednesday, 13:45 - 14:10 h, Room: H 0112, Talk 2

Michael Patriksson
Nonlinear continuous resource allocation - A numerical study

Coauthor: Christoffer Strömberg


We study the performance of the most important algorithms for solving the strictly convex and separable resource allocation problem. This singly constrained problem arises in many applications, particularly as a subproblem, whence the search for extremely efficient solution procedures for the problem continues. We compare the performance of algorithms belonging to the relaxation, breakpoint and quasi-Newton classes of methods, for sizes up to about 100 Million variables, establishing that a new implementation of a relaxation algorithm utilizing a blended evaluation of the relaxed problem performs the best in general, having linear practical convergence even for very many variables.



Wednesday, 14:15 - 14:40 h, Room: H 0112, Talk 3

Marc C. Steinbach
Estimating material parameters by X-ray diffraction


X-ray diffraction is a standard method for quantitative material
analysis in areas like crystallography, chemistry, or biochemistry:
X-Ray exposure yields intensity distributions that depend on the
molecular structure and that can be measured with high precision
over a certain range of diffraction angles. Material parameters are
then obtained by suitable parameter estimation methods.
The talk presents the resulting class of typically ill-conditioned
constrained inverse problems and reports on the development and
implementation of a real time solution algorithm. Main components of the
algorithm include a Levenberg-Marquardt method, a truncated CG method
featuring certain projection techniques, and sparse linear algebra
exploiting the specific Jacobian structure. The post-optimality analysis
includes a detection of modeling redundancy and a covariance computation
based on an SVD or a QR decomposition with pivoting.


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