Optimization of the Matrix Fourier-Filter for a Class of Nonlinear Optical Models with an Integral Objective Functional

We consider a new formulation of the Fourier-filtering problem that uses matrix Fourier-filters as the controls in nonlinear optical models described by quasi-linear functional-differential diffusion equations. Solvability of the control problem is proved for various classes of matrix Fourier-filter...

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Veröffentlicht in:Computational mathematics and modeling Jg. 31; H. 3; S. 320 - 337
Hauptverfasser: Sazonova, S. V., Razgulin, A. V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2020
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Integrals
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear control
Nonlinear optics
Optimization
feedback
functional
numerical solution of optimization problem
Fourier-filtering
gradient
Fourier-filter control
functional-differential diffusion equation
matrix Fourier-filter
nonlinear optical models
ISSN:1046-283X, 1573-837X
Online-Zugang:Volltext
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Zusammenfassung:We consider a new formulation of the Fourier-filtering problem that uses matrix Fourier-filters as the controls in nonlinear optical models described by quasi-linear functional-differential diffusion equations. Solvability of the control problem is proved for various classes of matrix Fourier-filters with a time-integral objective functional. Differentiability of the functional with respect to the matrix Fourier-filter and convergence of a variant of the gradient projection method are proved. Examples of numerical simulation of controlled structure formation are presented, and the advantages of matrix Fourier-filters compared with traditional multiplier filters are demonstrated.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1046-283X
1573-837X
DOI:10.1007/s10598-020-09494-8