.png){kind=icon}
.png){kind=icon}
Return
HIGH-INDEX OPTIMIZATION-BASED SHRINKING DIMER METHOD FOR FINDING HIGH-INDEX SADDLE POINTS
.png){kind=icon}
PRE
AI
DOI：10.1137/19M1253356.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We present a high-index optimization-based shrinking dimer (HiOSD) method to compute index-k saddle points as a generalization of the optimization-based shrinking dimer method for index-1 saddle points [L. Zhang, Q. Du, and Z. Zheng, SIAM T. Sci. Comput., 38 (2016), pp. A528-A544]. We first formulate a minimax problem for an index-k saddle point that is a local maximum on a k-dimensional manifold and a local minimum on its orthogonal complement. The k-dimensional maximal subspace is spanned by the k eigenvectors corresponding to the smallest k eigenvalues of the Hessian, which can be constructed by the simultaneous Rayleigh-quotient minimization technique or the locally optimal block preconditioned conjugate gradient method. Under the minimax framework, we implement the Barzilai-Borwein gradient method to speed up the convergence. We demonstrate the efficiency of the HiOSD method for computing high-index saddle points by applying finite-dimensional examples and semilinear elliptic problems.
Keywords:
rare event
saddle point
Morse index
dimer method
minimax
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W