Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems

2022 ◽  
Author(s):  
Amar Andjouh ◽  
Mohand Ouamer Bibi
Keyword(s):  
Quadratic Minimization ◽  
Minimization Problems ◽  
Global Algorithm

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.

A new method for large-scale box constrained convex quadratic minimization problems

1995 ◽  
Vol 5 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Ana Friedlander ◽  
José Mario Martínez ◽  
Marcos Raydon
Keyword(s):  
Large Scale ◽  
New Method ◽  
Quadratic Minimization ◽  
Minimization Problems

scholarly journals Some remarks on duality and optimality of a class of constrained convex quadratic minimization problems

2017 ◽  
Vol 27 (2) ◽  
pp. 219-225
Author(s):  
Sudipta Roy ◽  
Sandip Chatterjee ◽  
R.N. Mukherjee
Keyword(s):  
Optimality Condition ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Global Optimality ◽  
Convex Quadratic Optimization ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Global Optimality Condition

In this paper the duality and optimality of a class of constrained convex quadratic optimization problems have been studied. Furthermore, the global optimality condition of a class of interval quadratic minimization problems has also been discussed.

scholarly journals A modified generalized residual method for minimization problems with errors of a known level in weakened norms

2015 ◽  
pp. 456-463
Author(s):  
А.А. Дряженков
Keyword(s):  
A Priori ◽  
A Priori Information ◽  
Error Level ◽  
Numerical Examples ◽  
Residual Method ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Priori Information ◽  
The Cost ◽  
Nonclassical Information

Предложен алгоритм численного решения задачи квадратичной минимизации на эллипсоиде, заданном в гильбертовом пространстве компактным оператором. Алгоритм представляет собой определенную трансформацию обобщенного метода невязки, предназначенную для применения в неклассических информационных условиях, когда априорная информация об уровне погрешности в операторе, задающем функционал, доступна лишь в нормах, ослабленных по сравнению с исходными. При этом сходимость алгоритма устанавливается в исходных нормах. Приводятся простейшие вычислительные иллюстрации. An algorithm is proposed for the numerical solution of a quadratic minimization problem on an ellipsoid specified in the Hilbert space by a compact operator. This algorithm is a certain transform of the generalized residual method designed previously for the application in nonclassical information conditions when {\it a priori} information on the error level in an operator defining the cost functional is available only in the norms being weaker than the original ones. At the same time, the convergence of the algorithm is proved in the original norms. A number of simple numerical examples are discussed.

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