Goldfarb, DonaldWen, ZaiwenYin, Wotao2018-06-192018-06-192008-01Goldfarb, Donald, Wen, Zaiwen and Yin, Wotao. "A Curvilinear Search Method for p-Harmonic Flows on Spheres." (2008) <a href="https://hdl.handle.net/1911/102084">https://hdl.handle.net/1911/102084</a>.https://hdl.handle.net/1911/102084The problem of finding p-harmonic flows arises in a wide range of applications including micromagnetics, liquid crystal theory, directional diffusion, and chromaticity denoising. In this paper, we propose an innovative curvilinear search method for minimizing p-harmonic energies over spheres. Starting from a flow (map) on the unit sphere, our method searches along a curve that lies on the sphere in a manner similar to a standard inexact line search descent method. We show that our method is globally convergent if the step length satisfies the Armijo-Wolfe conditions. Computational tests are presented to demonstrate the efficiency of the proposed method and a variant of it that uses Barzilai-Borwein steps.23 ppengTechnical report