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A stabilization procedure by line‐search computation for first order approximation strategies in structural optimization
Author(s) -
Mahnken R.,
Stein E.,
Bischoff D.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350505
Subject(s) - backtracking , line search , mathematical optimization , descent (aeronautics) , mathematics , divergence (linguistics) , descent direction , line (geometry) , computation , hessian matrix , convergence (economics) , function (biology) , algorithm , computer science , gradient descent , path (computing) , economic growth , aerospace engineering , linguistics , engineering , biology , philosophy , geometry , machine learning , evolutionary biology , artificial neural network , programming language , economics
The paper is concerned with first order approximation methods to solve non‐linear optimization problems as they arise in structural optimization. A modification of the original Method of Moving Asymptotes (MMA) is presented to prevent oscillation or divergence by incorporating a line‐search into the global iteration algorithm. In this line‐search a merit‐function of augmented Lagrangian type is decreased by using a backtracking strategy. A proof is presented to show the descent property of the proposed merit‐function for MMA. Numerical examples demonstrate how the new technique stabilizes the iteration process.