Quasi-Newton minimization for the -Laplacian problem

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• 作者：M. Caliari ; ^{marco.caliari@univr.it" class="auth_mail" title="E-mail the corresponding author} ; S. Zuccher ^{simone.zuccher@univr.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：p(x)p(x)-Laplacian ; Degenerate quasi-linear elliptic problem ; Quasi-Newton minimization
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：122-131
• 全文大小：1315 K

文摘

We propose a quasi-Newton minimization approach for the solution of the p(x)$p\left(x\right)$-Laplacian elliptic problem, x∈Ω⊂R^m$x\in \Omega \subset {\mathbb{R}}^m$. This method outperforms those existing for the p(x)$p\left(x\right)$-variable case, which are based on general purpose minimizers such as BFGS. Moreover, when compared to ad hoc   techniques available in literature for the p$p$-constant case, and usually referred to as “mesh independent”, the present method turns out to be generally superior thanks to better descent directions given by the quadratic model.