Global Optimization Solutions to a Class of Nonconvex Quadratic Minimization Problems with Quadratic Constraints

2017 ◽  
pp. 339-357
Author(s):  
Yu Bo Yuan
Keyword(s):  
Global Optimization ◽  
Quadratic Constraints ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Nonconvex Quadratic Minimization

scholarly journals First-Order Methods for Nonconvex Quadratic Minimization

SIAM Review ◽  
2020 ◽  
Vol 62 (2) ◽  
pp. 395-436
Author(s):  
Yair Carmon ◽  
John C. Duchi
Keyword(s):  
First Order ◽  
Quadratic Minimization ◽  
First Order Methods ◽  
Nonconvex Quadratic Minimization

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.

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