Mathematics > Optimization and Control
[Submitted on 30 Nov 2018 (v1), last revised 5 Dec 2018 (this version, v2)]
Title:Finding Zeros of Hölder Metrically Subregular Mappings via Globally Convergent Levenberg-Marquardt Methods
View PDFAbstract:We present two globally convergent Levenberg-Marquardt methods for finding zeros of Hölder metrically subregular mappings that may have non-isolated zeros. The first method unifies the Levenberg- Marquardt direction and an Armijo-type line search, while the second incorporates this direction with a nonmonotone trust-region technique. For both methods, we prove the global convergence to a first-order stationary point of the associated merit function. Furthermore, the worst-case global complexity of these methods are provided, indicating that an approximate stationary point can be computed in at most $\mathcal{O}(\varepsilon^{-2})$ function and gradient evaluations, for an accuracy parameter $\varepsilon>0$. We also study the conditions for the proposed methods to converge to a zero of the associated mappings. Computing a moiety conserved steady state for biochemical reaction networks can be cast as the problem of finding a zero of a Hölder metrically subregular mapping. We report encouraging numerical results for finding a zero of such mappings derived from real-world biological data, which supports our theoretical foundations.
Submission history
From: Ronan M.T. Fleming Dr [view email][v1] Fri, 30 Nov 2018 18:15:09 UTC (298 KB)
[v2] Wed, 5 Dec 2018 01:24:25 UTC (364 KB)
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