A nonmonotone spectral projected gradient method for large-scaletopology optimization problems

Rouhollah Tavakoli; Hongchao Zhang

doi:10.3934/naco.2012.2.395

Article Contents

2012, Volume 2, Issue 2: 395-412. Doi: 10.3934/naco.2012.2.395

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A nonmonotone spectral projected gradient method for large-scale topology optimization problems

Rouhollah Tavakoli^1, and
Hongchao Zhang^2,

1.
Department of Material Science and Engineering, Sharif University of Technology, Tehran, P.O. Box 11365-9466
2.
Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70808

Received: October 2011

Revised: March 2012

Published: April 2012

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Abstract

An efficient gradient-based method to solve the volume constrained topology optimization problems is presented. Each iterate of this algorithm is obtained by the projection of a Barzilai-Borwein step onto the feasible set consisting of box and one linear constraints (volume constraint). To ensure the global convergence, an adaptive nonmonotone line search is performed along the direction that is given by the current and projection point. The adaptive cyclic reuse of the Barzilai-Borwein step is applied as the initial stepsize. The minimum memory requirement, the guaranteed convergence property, and almost only one function and gradient evaluations per iteration make this new method very attractive within common alternative methods to solve large-scale optimal design problems. Efficiency and feasibility of the presented method are supported by numerical experiments.

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Mathematics Subject Classification: Primary: 90C06, 90C26; Secondary: 65Y20.

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