2023
DOI: 10.1007/s11425-021-2093-1
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Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs

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Cited by 1 publication
(3 citation statements)
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“…It is worthwhile to point out that step-size search rules used in traditional LMMs include the optimal/exact step-size search rule [26], the normalized Armijo-type step-size search rule [27,41,44], the normalized Goldstein-type step-size search rule [29] and the normalized Wolfe-Powelltype step-size search rules [30]. And up to now all step-size search rules in traditional LMMs are monotone in the sense that the sequence {E(w k )} is monotonically decreasing.…”
Section: Lemma 25 ([41]mentioning
confidence: 99%
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“…It is worthwhile to point out that step-size search rules used in traditional LMMs include the optimal/exact step-size search rule [26], the normalized Armijo-type step-size search rule [27,41,44], the normalized Goldstein-type step-size search rule [29] and the normalized Wolfe-Powelltype step-size search rules [30]. And up to now all step-size search rules in traditional LMMs are monotone in the sense that the sequence {E(w k )} is monotonically decreasing.…”
Section: Lemma 25 ([41]mentioning
confidence: 99%
“…And up to now all step-size search rules in traditional LMMs are monotone in the sense that the sequence {E(w k )} is monotonically decreasing. Actually this feature is vital for the convergence analysis in traditional LMMs, see [27,29,30,41,52]. Since the work of this paper is closely related to the normalized Armijo-type step-size search rule, let us describe it a little more.…”
Section: Lemma 25 ([41]mentioning
confidence: 99%
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