Premium
An Extension of the Conjugate Directions Method With Orthogonalization to Large‐Scale Problems With Bound Constraints
Author(s) -
Boudinov Edouard,
Manevich Arkadiy
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510343
Subject(s) - conjugate , orthogonalization , conjugate gradient method , extension (predicate logic) , minification , scale (ratio) , mathematics , conjugate residual method , mathematical optimization , upper and lower bounds , derivation of the conjugate gradient method , computer science , algorithm , mathematical analysis , artificial intelligence , physics , gradient descent , quantum mechanics , artificial neural network , programming language
In our previous works a new method of conjugate directions for large‐scale unconstrained minimization problems has been presented [1, 2]. In the paper this algorithm is extended to minimization problems with bound constraints. Because the linear minimization along the newly found conjugate vector is not needed for constructing the next conjugate vector and one arbitrarily step‐size (not necessarily the optimal one) is calculated along this conjugate direction, we are able to incorporate naturally the bound constraints into the algorithm. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)