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Trust regions based on conic functions in linear and nonlinear programming
Author(s) -
Nazareth J. L.
Publication year - 1995
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680020305
Subject(s) - conic section , nonlinear programming , interior point method , linear programming , mathematics , conjugate gradient method , mathematical optimization , ellipsoid , trust region , nonlinear system , minification , variety (cybernetics) , point (geometry) , algorithm , computer science , geometry , statistics , physics , computer security , quantum mechanics , astronomy , radius
Abstract An optimization method is developed based on ellipsoidal trust regions that are defined by conic functions. It provides a powerful unifying theory from which can be derived a variety of interesting and potentially useful optimization algorithms, in particular, conjugate‐gradient‐like algorithms for nonlinear minimization and Karmarkar‐like interior‐point algorithms for linear programming.