Geodesic
Use of hybrid algorithms in extremum eigenproblems of Lagrangian dynamical systems
Matematičeskoe modelirovanie i čislennye metody (2016), pp. 84-102.

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The study examines extremum problems for eigen spectra components of Lagrangian dynamical systems. Mathematical models of the systems studied are described by the matrices depending on the parameters. The eigenproblems defined for such systems, in general, are characterized by a spectrum, which can contain multiple eigenvalues. Subtests in extremum problems are assumed to be continuous, Lipschitzian, multiextremum and maybe not everywhere differentiable functions. The search for global solutions is conducted using new hybrid algorithms that combine a stochastic algorithm for scanning the variables space and deterministic local search methods. The study gives numerical examples of solving the problems of global nondifferentiable minimization of the maximum systems eigenvalues.
Keywords: eigenvalue, algebraic multiplicity, Lipschitz condition, smoothing approximation, global optimization, Metropolis algorithm, hybrid algorithm. 
@article{MMCM_2016_a5,
     author = {V. D. Sulimov and P. M. Shkapov and D. A. Goncharov},
     title = {Use of hybrid algorithms in extremum eigenproblems of {Lagrangian} dynamical systems},
     journal = {Matemati\v{c}eskoe modelirovanie i \v{c}islennye metody},
     pages = {84--102},
     publisher = {mathdoc},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMCM_2016_a5/}
}
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V. D. Sulimov; P. M. Shkapov; D. A. Goncharov. Use of hybrid algorithms in extremum eigenproblems of Lagrangian dynamical systems. Matematičeskoe modelirovanie i čislennye metody (2016), pp. 84-102. http://geodesic.mathdoc.fr/item/MMCM_2016_a5/