scholarly journals On Weak and Strong Convergence of the Projected Gradient Method for Convex Optimization in Real Hilbert Spaces

2016 ◽  
Vol 37 (2) ◽  
pp. 129-144 ◽  
Author(s):  
J. Y. Bello Cruz ◽  
W. De Oliveira
Keyword(s):  
Convex Optimization ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Gradient Method ◽  
Projected Gradient Method ◽  
Weak And Strong Convergence ◽  
Projected Gradient

scholarly journals Strong Convergence of a Projected Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shunhou Fan ◽  
Yonghong Yao
Keyword(s):  
Convex Optimization ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Projection Method ◽  
Minimization Problem ◽  
Gradient Method ◽  
Optimization Problems ◽  
Projected Gradient Method ◽  
Projected Gradient ◽  
Convex Optimization Problems

The projected-gradient method is a powerful tool for solving constrained convex optimization problems and has extensively been studied. In the present paper, a projected-gradient method is presented for solving the minimization problem, and the strong convergence analysis of the suggested gradient projection method is given.

An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression

2019 ◽  
Vol 36 (02) ◽  
pp. 1940008
Author(s):  
Jun Fan ◽  
Liqun Wang ◽  
Ailing Yan
Keyword(s):  
Gradient Method ◽  
Least Squares Method ◽  
Optimal Solution ◽  
High Dimensional ◽  
Sparse Signals ◽  
Projected Gradient Method ◽  
Constrained Least Squares ◽  
Projected Gradient ◽  
High Dimensional Case ◽  
Noisy Measurements

In this paper, we employ the sparsity-constrained least squares method to reconstruct sparse signals from the noisy measurements in high-dimensional case, and derive the existence of the optimal solution under certain conditions. We propose an inexact sparse-projected gradient method for numerical computation and discuss its convergence. Moreover, we present numerical results to demonstrate the efficiency of the proposed method.

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