학술논문

Finding zeros of Hölder metrically subregular mappings via globally convergent Levenberg–Marquardt methods.
Document Type
Article
Source
Optimization Methods & Software. Feb2022, Vol. 37 Issue 1, p113-149. 37p.
Subject
*REGULAR graphs
*NONLINEAR equations
*MOIETIES (Chemistry)
Language
ISSN
1055-6788
Abstract
We introduce LMLS and LMQR, 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 non-monotone quadratic regularization 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 O (ε − 2) function and gradient evaluations, for an accuracy parameter ε > 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. [ABSTRACT FROM AUTHOR]