scholarly journals RETRACTED: Global optimization solutions to a class of non-convex quadratic minimization problems with quadratic constraints

2015 ◽  
Vol 21 (3) ◽  
pp. NP206-NP207
Author(s):  
Yubo Yuan
Keyword(s):  
Global Optimization ◽  
Quadratic Constraints ◽  
Quadratic Minimization ◽  
Minimization Problems

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.

NEW ADAPTIVE BARZILAI–BORWEIN STEP SIZE AND ITS APPLICATION IN SOLVING LARGE-SCALE OPTIMIZATION PROBLEMS

2018 ◽  
Vol 61 (1) ◽  
pp. 76-98 ◽  
Author(s):  
TING LI ◽  
ZHONG WAN
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Test Problems ◽  
Large Scale Optimization ◽  
Step Size ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Ill Posed ◽  
Scale Optimization

We propose a new adaptive and composite Barzilai–Borwein (BB) step size by integrating the advantages of such existing step sizes. Particularly, the proposed step size is an optimal weighted mean of two classical BB step sizes and the weights are updated at each iteration in accordance with the quality of the classical BB step sizes. Combined with the steepest descent direction, the adaptive and composite BB step size is incorporated into the development of an algorithm such that it is efficient to solve large-scale optimization problems. We prove that the developed algorithm is globally convergent and it R-linearly converges when applied to solve strictly convex quadratic minimization problems. Compared with the state-of-the-art algorithms available in the literature, the proposed step size is more efficient in solving ill-posed or large-scale benchmark test problems.

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