Necessary Extremum Conditions (Euler-Lagrange Equation)

1972 ◽  
pp. 38-42
Author(s):  
Igor Vladimirovich Girsanov ◽  
B. T. Poljak
Keyword(s):  
Lagrange Equation ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions

Analysis of 2-D Impedance Cloaking Problem Based on Boundary Element Method

2014 ◽  
Vol 635-637 ◽  
pp. 3-6
Author(s):  
Gennady V. Alekseev ◽  
Andrei Baydin ◽  
Olga Larkina
Keyword(s):  
Boundary Element Method ◽  
Control Problem ◽  
Boundary Element ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Optimality System ◽  
Homogenous Medium ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions ◽  
Element Method

Control problems are considered for a two-dimensional model describing wave scattering in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The solvability of the original scattering problem for 2-D Helmholtz equation and of the control problem is proved. Optimality system dгescribing the necessary extremum conditions are derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

Boundary Element Approach in Impedance Cloaking Problem

2015 ◽  
Vol 756 ◽  
pp. 524-528
Author(s):  
Andrei Baydin ◽  
Olga Larkina
Keyword(s):  
Boundary Element ◽  
Extremal Problem ◽  
Surface Impedance ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Optimality System ◽  
Homogenous Medium ◽  
Element Approach ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions

The cloaking problem is considered for a 2-D wave scattering model in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The problem is reduced to the inverse extremal problem of choosing the surface impedance. The solvability of the original scattering problem for 2-D Helmholtz equation and of the extremal problem is proved. Optimality system describing the necessary extremum conditions is derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

On an Euler-Lagrange equation for color to grayscale conversion

2019 ◽  
Vol 2019 (1) ◽  
pp. 95-98
Author(s):  
Hans Jakob Rivertz
Keyword(s):  
Variational Inequality ◽  
Color Image ◽  
Lagrange Equation ◽  
New Method ◽  
Grayscale Image ◽  
Structure Tensors

In this paper we give a new method to find a grayscale image from a color image. The idea is that the structure tensors of the grayscale image and the color image should be as equal as possible. This is measured by the energy of the tensor differences. We deduce an Euler-Lagrange equation and a second variational inequality. The second variational inequality is remarkably simple in its form. Our equation does not involve several steps, such as finding a gradient first and then integrating it. We show that if a color image is at least two times continuous differentiable, the resulting grayscale image is not necessarily two times continuous differentiable.

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