Quasi-Newton minimization for the \(p(x)\)-Laplacian problem. (English) Zbl 1462.90152
Summary: We propose a quasi-Newton minimization approach for the solution of the \(p(x)\)-Laplacian elliptic problem, \(x \in \Omega \subset \mathbb{R}^m\). This method outperforms those existing for the \(p(x)\)-variable case, which are based on general purpose minimizers such as BFGS. Moreover, when compared to ad hoc techniques available in literature for the \(p\)-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.
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