iterative optimization
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Author(s):  
Pontus Giselsson ◽  
Walaa M. Moursi

AbstractMany iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.


Cryobiology ◽  
2021 ◽  
Vol 103 ◽  
pp. 172
Author(s):  
Frankie Tu ◽  
Mohsen Sharafi ◽  
Maajid Bhat ◽  
Patrick Vincent ◽  
Patrick Blondin ◽  
...  

2021 ◽  
Author(s):  
Mou Wang ◽  
Daojin Chen ◽  
Xuecheng Zhang ◽  
Shunjun Wei ◽  
Jun Shi ◽  
...  

2021 ◽  
Vol 2015 (1) ◽  
pp. 012047
Author(s):  
Giorgio Gnecco ◽  
Andrea Bacigalupo ◽  
Francesca Fantoni ◽  
Daniela Selvi

Abstract A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based iterative optimization algorithms to the numerical solution of such problems is typically highly demanding, due to the complexity of the underlying physical models. Nevertheless, supervised machine learning techniques can reduce such a computational effort, e.g., by replacing the original objective functions of such optimization problems with more-easily computable approximations. In this framework, the present article describes the application of a related unsupervised machine learning technique, namely, principal component analysis, to approximate the gradient of the objective function of a band gap optimization problem for an acoustic metamaterial, with the aim of making the successive application of a gradient-based iterative optimization algorithm faster. Numerical results show the effectiveness of the proposed method.


2021 ◽  
pp. 1-17
Author(s):  
J. Justin Wilbanks ◽  
Ryan A. Schultz ◽  
Brian C. Owens

2021 ◽  
Vol 144 ◽  
pp. 106630
Author(s):  
Jianhui Huang ◽  
An Pan ◽  
Huiliang Jin ◽  
Guoxiang Meng ◽  
Qian Ye

Author(s):  
Shashwat Gupta ◽  
Andrés D. Román-Ospino ◽  
Yukteshwar Baranwal ◽  
Douglas Hausner ◽  
Rohit Ramachandran ◽  
...  

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