Boggs, Paul T.; Gay, David M.; Griffiths, Stewart K.; Lewis, Robert Michael; Long, Kevin R.; Nash, Stephen; Nilson, Robert H. Optimization algorithms for hierarchical problems with application to nano-porous materials. (Optimization algorithms for hierarchical problems with application to nanoporous materials.) (English) Zbl 1266.49064 SIAM J. Optim. 22, No. 4, 1285-1308 (2012). Authors’ abstract: We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nano-porous materials. Nano-porous materials have a broad range of engineering applications, including gas storage and filtration, electrical energy storage in batteries and capacitors, and catalysis. The design of such materials involves modeling of the material over many length scales, leading to a hierarchy of mathematical models. Our algorithms are also hierarchical in structure with the goal of exploiting the model hierarchy to obtain solutions more rapidly. We discuss the choice of optimization models, initialization schemes, a hierarchical optimization algorithm, software design, and computational results. Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) Cited in 3 Documents MSC: 49M37 Numerical methods based on nonlinear programming 49M15 Newton-type methods 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:multigrid optimization; multilevel optimization; nonlinear optimization; complex hierarchical optimization Software:Trilinos PDFBibTeX XMLCite \textit{P. T. Boggs} et al., SIAM J. Optim. 22, No. 4, 1285--1308 (2012; Zbl 1266.49064) Full Text: DOI