scholarly journals Bregman Proximal Gradient Algorithm With Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 126515-126529
Author(s):  
Xiaoya Zhang ◽  
Roberto Barrio ◽  
M. Angeles Martinez ◽  
Hao Jiang ◽  
Lizhi Cheng
Keyword(s):  
Gradient Algorithm ◽  
Minimization Problems ◽  
Proximal Gradient Algorithm ◽  
Nonsmooth Minimization

Numerical experiments on stochastic block proximal-gradient type method for convex constrained optimization involving coordinatewise separable problems

2019 ◽  
Vol 35 (3) ◽  
pp. 371-378
Author(s):  
PORNTIP PROMSINCHAI ◽  
NARIN PETROT ◽  
◽  
◽  
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Objective Functions ◽  
Constrained Optimization Problems ◽  
Type Method ◽  
Coordinate Descent Algorithm ◽  
Proximal Gradient Algorithm ◽  
Separable Problems ◽  
Gradient Type

In this paper, we consider convex constrained optimization problems with composite objective functions over the set of a minimizer of another function. The main aim is to test numerically a new algorithm, namely a stochastic block coordinate proximal-gradient algorithm with penalization, by comparing both the number of iterations and CPU times between this introduced algorithm and the other well-known types of block coordinate descent algorithm for finding solutions of the randomly generated optimization problems with regularization term.

Generalized ordered linear regression with regularization

2012 ◽  
Vol 60 (3) ◽  
pp. 481-489 ◽  
Author(s):  
J.M. Łęski ◽  
N. Henzel
Keyword(s):  
Linear Regression ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Gradient Algorithm ◽  
Weighted Averaging ◽  
Criterion Function ◽  
Regression Problem ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Model Residuals

Abstract Linear regression analysis has become a fundamental tool in experimental sciences. We propose a new method for parameter estimation in linear models. The ’Generalized Ordered Linear Regression with Regularization’ (GOLRR) uses various loss functions (including the ǫ-insensitive ones), ordered weighted averaging of the residuals, and regularization. The algorithm consists in solving a sequence of weighted quadratic minimization problems where the weights used for the next iteration depend not only on the values but also on the order of the model residuals obtained for the current iteration. Such regression problem may be transformed into the iterative reweighted least squares scenario. The conjugate gradient algorithm is used to minimize the proposed criterion function. Finally, numerical examples are given to demonstrate the validity of the method proposed.

scholarly journals Properties and Iterative Methods for theQ-Lasso

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Mohammad Ali Alghamdi ◽  
Naseer Shahzad ◽  
Hong-Kun Xu
Keyword(s):  
Iterative Methods ◽  
Convex Subset ◽  
Gradient Algorithm ◽  
Tuning Parameter ◽  
Linear Measurements ◽  
Tolerance Level ◽  
Basic Properties ◽  
Proximal Gradient Algorithm ◽  
Signal Image

We introduce theQ-lasso which generalizes the well-known lasso of Tibshirani (1996) withQa closed convex subset of a Euclideanm-space for some integerm≥1. This setQcan be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image via the lasso. Solutions of theQ-lasso depend on a tuning parameterγ. In this paper, we obtain basic properties of the solutions as a function ofγ. Because of ill posedness, we also applyl1-l2regularization to theQ-lasso. In addition, we discuss iterative methods for solving theQ-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm.

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