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Starting‐point strategy for interior‐point algorithms for lower‐bound shakedown analysis
Author(s) -
Simon JaanWillem,
Weichert Dieter,
Höwer Daniel
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110132
Subject(s) - shakedown , convergence (economics) , interior point method , mathematical optimization , point (geometry) , upper and lower bounds , mathematics , nonlinear system , algorithm , regular polygon , computer science , engineering , finite element method , geometry , mathematical analysis , physics , structural engineering , quantum mechanics , economics , economic growth
Shakedown analysis by using the lower‐bound theorem leads to computationally intensive nonlinear convex optimization problems with a large number of unknowns and constraints. Interior‐point algorithms such as recently developed by the authors have proven to be efficient for the solution of these problems. For convergence and efficiency of the iterative process of these algorithms the choice of the starting‐point is crucial. It should be inside of the feasible region and well‐centered for fast convergence. No general method exists for the construction of optimum starting‐points and only few investigations have been published on this issue. In this paper the physical meaning of the involved variables in shakedown problems is used to optimize starting‐points. The efficiency of the new method is illustrated by a numerical examples and comparison with an alternative approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)