scholarly journals Second order sweeping process with almost convex perturbation

2019 ◽  
Author(s):  
Doria Affane ◽  
Mustapha Fateh Yarou
Keyword(s):  
Second Order ◽  
Sweeping Process ◽  
Almost Convex ◽  
Convex Perturbation

Reduction approach to second order perturbed state-dependent sweeping process

2019 ◽  
Vol 28 (2) ◽  
Author(s):  
MUSTAPHA FATEH YAROU
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sweeping Process ◽  
New Approach ◽  
Standard Methods ◽  
First Order ◽  
Finite Dimensional ◽  
Perturbed State ◽  
State Dependent

In this paper, we present a new approach to solving second order nonconvex perturbed sweeping process in finite dimensional setting. It consists in a reduction of the problem to a first order one without use of the standard methods of fixed point theory. The perturbation, that is the external force applied on the system is not necessary with bounded values.

Response Analysis of Acoustic Field With Convex Parameters

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu
Keyword(s):  
Perturbation Method ◽  
Acoustic Field ◽  
Taylor Series ◽  
Optimization Method ◽  
Second Order ◽  
Response Analysis ◽  
Engineering Practice ◽  
Local Optima ◽  
First Order ◽  
Convex Perturbation

The acoustic field with convex parameters widely exists in the engineering practice. The vertex method and the anti-optimization method are not considered as appropriated approaches for the response analysis of acoustic field with convex parameters. The shortcoming of the vertex method is that the local optima out of vertexes cannot be identified. The disadvantage of the anti-optimization method is that the analytical formulation of response may be not obtained. To analyze the acoustic field with convex parameters efficiently and effectively, a first-order convex perturbation method (FCPM) and a second-order convex perturbation method (SCPM) are presented. In FCPM, the response of the acoustic field with convex parameters is expanded with the first-order Taylor series. In SCPM, the response of the acoustic field with convex parameters is expanded with the second-order Taylor series neglecting the nondiagonal elements of Hessian matrix. The variational bounds of the expanded responses in FCPM and SCPM are yielded by the Lagrange multiplier method. The accuracy and efficiency of FCPM and SCPM are investigated by numerical examples.

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