Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs

The local minimax method (LMM) proposed by Li and Zhou (2001) (2002) is an efficient to solve nonlinear elliptic partial differential equations (PDEs) with certain variational structures for multiple solutions. steepest descent direction the Armijo-type step-size search rules are adopted in play a significant role performance convergence analysis of traditional LMMs. In this paper, new algorithm framework LMMs established based on general directions two normalized (strong) Wolfe-Powell-type rules. corresponding named as LMM (NWP-LMM) introduced its feasibility global rigorously justified directions. As special case, NWP-LMM combined preconditioned (PSD) also verified. Consequently, it extends addition, conjugate gradient-type (CG-type) utilized speed up algorithm. Finally, extensive numerical results several semilinear PDEs reported profile their unstable solutions compared different algorithms LMM’s family indicate effectiveness robustness our algorithms. practice, CG-type indeed performs much better than known companions.