Application of the clipping procedure to the binary minimization of a quadratic functional

Kryzhanovskii, B. V.; Крыжановский, В М; Mikaélyan, A L

doi:10.1134/s1064562407020354

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…The second necessary expression relates the depth and width of a minimum. As shown in [14], the width of a minimum E 0 increases with its depth. Correspondingly, the probability to find this minimum grows exponentially as P (E 0 ) ∼ exp −N E 2 c /E 2 0 .…”

Section: Basic Relationsmentioning

confidence: 85%

“…From r 0 ≥ r c it follows that γ ≥ 0.3 √ N . This means that the probability of the minimum's deepening Pr {E 20 < E 0 } approaches unity with increasing N. In other words, the surface transformation is most likely to cause the minimum to deepen considerably (by a factor of 1.35 on average), which, according to [14], leads to the probability of finding the global minimum increasing exponentially with N .…”

Section: A the Deepening Of The Minimamentioning

confidence: 99%

“…The successful solution of the traveling salesman problem [3] with the Hopfield neural network introduced neural-net methods in graph theory [4], image processing [5] and other fields [6][7][8][9][10][11][12][13]. The reasons for such a successful application are studied in [14] where the probability of finding a minimum in random search is shown to grow exponentially with the depth of the minimum. In particular, when a neural network is initialized at random, it is very likely to converge to a state corresponding to the global minimum or to a local minimum whose depth is comparable to that of the global minimum [15,16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Increasing the attraction area of the global minimum in the binary optimization problem

Karandashev

Kryzhanovsky

2012

J Glob Optim

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The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power the matrix it is based on. We demonstrate that this brings about changes of the energy surface: deep minima displace slightly in the space and become still deeper and their attraction areas grow significantly. Experiments show that this approach results in a considerable displacement of the spectrum of the sought-for minima to the area of greater depth, and the probability of finding the global minimum increases abruptly (by a factor of 10 3 in the case of the 10 × 10 Edwards-Anderson spin glass).

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Section: Basic Relationsmentioning

confidence: 85%

Section: A the Deepening Of The Minimamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Increasing the attraction area of the global minimum in the binary optimization problem

Karandashev

Kryzhanovsky

2012

J Glob Optim

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Cluster Domains in Binary Minimization Problems

Litinskii¹

2007

Lecture Notes in Computer Science

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New Methods for Control System Signal Sampling in Neural Networks of Power Facilities

2020

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The authors of the paper emphasize that when the Nyquist-Shannon sampling theorem is used in practice, there arise several problems, which can be explained only through the use of new methodologies and mathematical models. The review of the researchers' works, as well as the authors' own practical research in the course of processing the statistical sample, which is described by a wave-like sine-cosine function, leads to the conclusion that it is necessary to take into account optimization criteria for high-tech processes and innovative indicators of building functions for the statistical sample, for example, when signals are transmitted and sampled using neural networks at production facilities. In the practice of economic calculations, for example, when making a graphic presentation of trend lines based on the functions built subject to the sampling conditions by the Nyquist theorem, the authors propose to use new methods for approximating piece linear functions, which allow for achieving a smaller error as compared to standard calculation methods. The work resulted in the creation of a neural network regulation algorithm, which will be trained based on the collected data and adapted to a specific type of a boiler unit. Besides, it was established that the task of neural network algorithms in the program is to find the optimal value of the weight coefficient for each argument of the resulting function to obtain the maximum number of predictions of the flare level and the particle burn-up time, which are consistent with reality. The use of these methods for the first time made it possible to significantly reduce the error, which is confirmed not only by calculations, but also by experimental data.

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Application of the clipping procedure to the binary minimization of a quadratic functional

Cited by 6 publications

References 5 publications

Increasing the attraction area of the global minimum in the binary optimization problem

Increasing the attraction area of the global minimum in the binary optimization problem

Cluster Domains in Binary Minimization Problems

New Methods for Control System Signal Sampling in Neural Networks of Power Facilities

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