论文标题
针对涉及$ p（x）$ - 拉普拉斯运算符的一类优化问题的预处理最深的下降算法
A preconditioned deepest descent algorithm for a class of optimization problems involving the $p(x)$-Laplacian operator
论文作者
论文摘要
在本文中，我们关注的是涉及$ p（x）$ laplacian运算符的一类优化问题，这些问题在成像和信号分析中出现。考虑到可变指数$ p（x）$是log-hölder的连续函数，我们研究了合并空间中这种问题的良好性。此外，我们为问题的数值解决方案提出了一种预处理的下降算法，考虑到有限维度空间中的“冷冻指数”方法。最后，我们进行了几个数值实验，以显示我们方法的优势。具体而言，我们研究了两个详细的示例，它们的动机在于提出的技术可能扩展到图像处理。
In this paper we are concerned with a class of optimization problems involving the $p(x)$-Laplacian operator, which arise in imaging and signal analysis. We study the well-posedness of this kind of problems in an amalgam space considering that the variable exponent $p(x)$ is a log-Hölder continuous function. Further, we propose a preconditioned descent algorithm for the numerical solution of the problem, considering a "frozen exponent" approach in a finite dimension space. Finally, we carry on several numerical experiments to show the advantages of our method. Specifically, we study two detailed example whose motivation lies in a possible extension of the proposed technique to image processing.
