scholarly journals Perturbation Techniques for Convergence Analysis of Proximal Gradient Method and Other First-Order Algorithms via Variational Analysis

2021 ◽  
Author(s):  
Xiangfeng Wang ◽  
Jane J. Ye ◽  
Xiaoming Yuan ◽  
Shangzhi Zeng ◽  
Jin Zhang
Keyword(s):  
Convergence Analysis ◽  
Gradient Method ◽  
Variational Analysis ◽  
Perturbation Techniques ◽  
Proximal Gradient Method ◽  
First Order

A note on the accelerated proximal gradient method for nonconvex optimization

2018 ◽  
Vol 34 (3) ◽  
pp. 449-457
Author(s):  
HUIJUAN WANG ◽  
◽  
HONG-KUN XU ◽  
Keyword(s):  
Machine Learning ◽  
Objective Function ◽  
Convergence Analysis ◽  
Nonconvex Optimization ◽  
Gradient Method ◽  
Optimization Problem ◽  
Proximal Gradient Method ◽  
International Conference ◽  
Variable Stepsizes ◽  
Sydney Australia

We improve a recent accelerated proximal gradient (APG) method in [Li, Q., Zhou, Y., Liang, Y. and Varshney, P. K., Convergence analysis of proximal gradient with momentum for nonconvex optimization, in Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, PMLR 70, 2017] for nonconvex optimization by allowing variable stepsizes. We prove the convergence of the APG method for a composite nonconvex optimization problem under the assumption that the composite objective function satisfies the Kurdyka-Łojasiewicz property.

Distributed proximal-gradient method for convex optimization with inequality constraints

2015 ◽  
Vol 56 ◽  
pp. 160 ◽  
Author(s):  
Jueyou Li ◽  
Changzhi Wu ◽  
Zhiyou Wu ◽  
Qiang Long ◽  
Xiangyu Wang
Keyword(s):  
Convex Optimization ◽  
Gradient Method ◽  
Inequality Constraints ◽  
Proximal Gradient Method

scholarly journals Learned Collaborative Stereo Refinement

2021 ◽  
Author(s):  
Patrick Knöbelreiter ◽  
Thomas Pock
Keyword(s):  
Structural Properties ◽  
Gradient Method ◽  
Color Image ◽  
Image Space ◽  
Activation Functions ◽  
Disparity Map ◽  
Proximal Gradient Method ◽  
Variational Structure ◽  
Disparity Maps ◽  
The Individual

AbstractIn this work, we propose a learning-based method to denoise and refine disparity maps. The proposed variational network arises naturally from unrolling the iterates of a proximal gradient method applied to a variational energy defined in a joint disparity, color, and confidence image space. Our method allows to learn a robust collaborative regularizer leveraging the joint statistics of the color image, the confidence map and the disparity map. Due to the variational structure of our method, the individual steps can be easily visualized, thus enabling interpretability of the method. We can therefore provide interesting insights into how our method refines and denoises disparity maps. To this end, we can visualize and interpret the learned filters and activation functions and prove the increased reliability of the predicted pixel-wise confidence maps. Furthermore, the optimization based structure of our refinement module allows us to compute eigen disparity maps, which reveal structural properties of our refinement module. The efficiency of our method is demonstrated on the publicly available stereo benchmarks Middlebury 2014 and Kitti 2015.

scholarly journals Aanalytical Solution for Motion Around Radiated Varying Mass Body

2019 ◽  
Vol 16 ◽  
pp. 8407-8419
Author(s):  
Marwa Abdullah Bin Humaidan ◽  
M. I. El-Saftawy ◽  
H. M. Asiri
Keyword(s):  
Time Series ◽  
Radiation Pressure ◽  
Pressure Effect ◽  
Hamiltonian Function ◽  
Perturbation Techniques ◽  
First Order ◽  
D Operator ◽  
Order Solution ◽  
Delaunay Variables ◽  
Varying Mass

In this work we will add the radiation pressure effect of varying mass body to the model of varying mass Hamiltonian function, including Periastron effect. The problem was formulated in terms of Delaunay variables. The solution of the problem was constructed based on Delava – Hansilmair perturbation techniques. Finally we find the first order solution for the problem as time series by calculating the desired order for the D operator and variables.

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