By Frits C. R. Spieksma (auth.), Panos M. Pardalos, Leonidas S. Pitsoulis (eds.)
Nonlinear task difficulties (NAPs) are ordinary extensions of the vintage Linear task challenge, and regardless of the efforts of many researchers during the last 3 a long time, they nonetheless stay the various toughest combinatorial optimization difficulties to unravel precisely. the aim of this publication is to supply in one quantity, significant algorithmic points and purposes of NAPs as contributed by way of major foreign specialists.
The chapters incorporated during this publication are fascinated by significant functions and the most recent algorithmic answer ways for NAPs. Approximation algorithms, polyhedral equipment, semidefinite programming techniques and heuristic systems for NAPs are incorporated, whereas purposes of this challenge category within the components of multiple-target monitoring within the context of army surveillance platforms, of experimental excessive strength physics, and of parallel processing are provided.
Audience: Researchers and graduate scholars within the parts of combinatorial optimization, mathematical programming, operations examine, physics, and computing device science.
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Extra resources for Nonlinear Assignment Problems: Algorithms and Applications
And Poore, A. B. (1998). Computational experiences with hot starts for a moving window implementation of track maintenance. In 1998 SPIE Conference Proceedings 3373, Signal and Data Processing of Small Targets 1998, Orlando, FL. [Shor, 1985] Shor, N. Z. (1985). Minimization Methods for Non-Differentiable Functions. Springer-Verlag, New York. [Sittler, 1964] Sittler, R. W. (1964). An optimal data association problem in surveillance theory. IEEE Transactions on Military Electronics, 8(2): 125139.
The assignment problem is of dimension N + 1 where N is the number of frames of observations in front of the existing tracks. The same window is being used to initiate new tracks and continue existing ones. A newer approach is based on the belief that once a track is well established, only a few frames are needed to benefit from the soft decisions on track continuation while a longer window is needed for track initiation. Thus, if the current frame is numbered k with frames k + 1, ... , k + N being for track continuation, one can go back to frames k M, ...
Thus the dimension of the assignment problem grows with the number of frames of data N. Processing all of the data at once is called batch processing, which eventually becomes computationally unacceptable as the dimension N increases. To circumvent this problem, we have introduced a sliding window in which data association decisions are hard prior to the window and soft within the window. , 1992] and refined in [Poore and Drummond, 1997J to include a dual pane window. We briefly discuss the single pane sliding window here and then refinements in the last subsection of this section.