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В.Д. Сулимов, П.М. Шкапов, А.В. Сулимов
64
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 5
OPTIMIZATION OF SINGULAR VALUES OF PARAMETER
DEPENDENT MATRICES USING HYBRID ALGORITHMS
V.D. Sulimov
1
P.M. Shkapov
1
spm@bmstu.ruA.V. Sulimov
2
1
Bauman Moscow State Technical University, Moscow, Russian Federation
2
Lomonosov Moscow State University, Branch, Sevastopol,
Russian Federation
Abstract
Keywords
This article considers extremal problems for singular spec-
trum components of real-valued matrices depending on
parameters. Criterion functions are supposed to be conti-
nuous, Lipschitzian, multiextremal and not necessarily dif-
ferentiable. While searching for global solutions we used new
hybrid algorithms that combine a stochastic algorithm for
scanning a search space and deterministic methods for local
search. The first hybrid algorithm determines local solutions
using the linearization method with smoothing approxima-
tions. The second algorithm does it by using the modified
space-filling curve method. Our work provides numerical
examples
Singular value, criterion function,
Lipschitzian constant, smoothing
approximation, Peano curve,
global optimization, Metropolis
algorithm, hybrid algorithm
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DOI: 10.1088/1742-6596/410/1/012015