2018/11/30 by Masoud Ahookhosh, Ahookhosh, Masoud, Ronan M. T. Fleming +3 · 2 citations
Computer Science · Mathematics · #65K05 #68Q25 #90C26 #Advanced Optimization Algorithms Research #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Metaheuristic Optimization Algorithms Research #Molecular Networks (q-bio.MN) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1812.00818
openalex publication_date 2018/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present two globally convergent Levenberg-Marquardt methods for finding\nzeros of H "older metrically subregular mappings that may have non-isolated\nzeros. The first method unifies the Levenberg- Marquardt direction and an\nArmijo-type line search, while the second incorporates this direction with a\nnonmonotone trust-region technique. For both methods, we prove the global\nconvergence to a first-order stationary point of the associated merit function.\nFurthermore, the worst-case global complexity of these methods are provided,\nindicating that an approximate stationary point can be computed in at most\n\O(\ε-2) function and gradient evaluations, for an\naccuracy parameter \ε>0. We also study the conditions for the\nproposed methods to converge to a zero of the associated mappings. Computing a\nmoiety conserved steady state for biochemical reaction networks can be cast as\nthe problem of finding a zero of a H "older metrically subregular mapping. We\nreport encouraging numerical results for finding a zero of such mappings\nderived from real-world biological data, which supports our theoretical\nfoundations.\n