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http://hdl.handle.net/10397/93320
Title: | Extended newton methods for multiobjective optimization : majorizing function technique and convergence analysis | Authors: | Wang, J Hu, Y Yu, CKW Li, C Yang, X |
Issue Date: | 2019 | Source: | SIAM journal on optimization, 2019, v. 29, no. 3, p. 2388-2421 | Abstract: | We consider the extended Newton method for approaching a Pareto optimum of a multiobjective optimization problem, establish quadratic convergence criteria, and estimate a radius of convergence ball under the assumption that the Hessians of objective functions satisfy an L-average Lipschitz condition. These convergence theorems significantly improve the corresponding ones in [J. Fliege, L. M. G. Drummond, and B. F. Svaiter, SIAM J. Optim., 20 (2009), pp. 602-626]. As applications of the obtained results, convergence theorems under the classical Lipschitz condition or the γ-condition are presented for multiobjective optimization, and the global quadratic convergence results of the extended Newton method with Armijo/Goldstein/Wolfe line-search schemes are also provided. | Keywords: | Convergence criteria L-average Lipschitz condition Multiobjective optimization Newton method Pareto optimum |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/18M1191737 | Rights: | © 2019 Society for Industrial and Applied Mathematics The following publication Wang, J., Hu, Y., Wai Yu, C. K., Li, C., & Yang, X. (2019). Extended Newton methods for multiobjective optimization: majorizing function technique and convergence analysis. SIAM Journal on Optimization, 29(3), 2388-2421 is available at https://doi.org/10.1137/18M1191737 |
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