Level set methods for finding critical points of mountain pass type
Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for...
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| Veröffentlicht in: | Nonlinear analysis 2011-08, Vol.74 (12), p.4058-4082 |
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| container_title | Nonlinear analysis |
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| creator | Lewis, Adrian S. Pang, C.H. Jeffrey |
| description | Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for addressing the Wilkinson problem of calculating the distance from a matrix to a closest matrix with repeated eigenvalues. Finally, we relate critical points of mountain pass type to nonsmooth and metric critical point theory. |
| doi_str_mv | 10.1016/j.na.2011.03.039 |
| format | Article |
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Jeffrey</creator><creatorcontrib>Lewis, Adrian S. ; Pang, C.H. Jeffrey</creatorcontrib><description>Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for addressing the Wilkinson problem of calculating the distance from a matrix to a closest matrix with repeated eigenvalues. 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| ispartof | Nonlinear analysis, 2011-08, Vol.74 (12), p.4058-4082 |
| issn | 0362-546X 1873-5215 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Critical point Eigenvalues Exact sciences and technology Mathematical analysis Mathematical models Mathematics Metric critical point theory Mountain pass Mountains Nonlinearity Nonsmooth critical points Partial differential equations Sciences and techniques of general use Strategy Superlinear convergence Wilkinson distance |
| title | Level set methods for finding critical points of mountain pass type |
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