Mathematical Investigation of Nonsmooth Optimization Algorithm in Elastodynamic Contact Problems with Friction for Bodies with Cracks

2003 ◽  
Vol 4 (4) ◽  
Author(s):  
V.V. Zozulya
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Algorithm ◽  
Contact Problems ◽  
Mathematical Investigation

scholarly journals Spherical Mesh Adaptive Direct Search for Separating Quasi-Uncorrelated Sources by Range-Based Independent Component Analysis

2013 ◽  
Vol 25 (9) ◽  
pp. 2486-2522 ◽  
Author(s):  
S. Easter Selvan ◽  
Pierre B. Borckmans ◽  
A. Chattopadhyay ◽  
P.-A. Absil
Keyword(s):  
Independent Component Analysis ◽  
Nonsmooth Optimization ◽  
Optimization Algorithm ◽  
Component Analysis ◽  
Direct Search ◽  
Independent Component ◽  
Mesh Adaptive Direct Search ◽  
Local Optima ◽  
Contrast Function ◽  
Unit Norm

It is seemingly paradoxical to the classical definition of the independent component analysis (ICA), that in reality, the true sources are often not strictly uncorrelated. With this in mind, this letter concerns a framework to extract quasi-uncorrelated sources with finite supports by optimizing a range-based contrast function under unit-norm constraints (to handle the inherent scaling indeterminacy of ICA) but without orthogonality constraints. Albeit the appealing contrast properties of the range-based function (e.g., the absence of mixing local optima), the function is not differentiable everywhere. Unfortunately, there is a dearth of literature on derivative-free optimizers that effectively handle such a nonsmooth yet promising contrast function. This is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit-norm columns with the following objectives: to ascertain convergence to a Clarke stationary point of the contrast function and adhere to the necessary unit-norm constraints more naturally. The proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search (MADS) method to handle locally Lipschitz objective functions defined on the sphere. The applicability of the algorithm in the ICA domain is demonstrated with simulations involving natural, face, aerial, and texture images.

scholarly journals An incremental nonsmooth optimization algorithm for clustering using L_1 and L_\infty norms

2020 ◽  
Vol 16 (6) ◽  
pp. 2757-2779
Author(s):  
Burak Ordin ◽  
◽  
Adil Bagirov ◽  
Ehsan Mohebi ◽  
◽  
...  
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Algorithm
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