Extended Newton methods for multiobjective optimization: majorizing function technique and convergence analysis: Newton methods for multiobjective optimization

Jinhua Wang, Yaohua Hu (Corresponding Author), Carisa Kwok Wai Yu, Chong Li, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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 \gamma -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.
Original languageEnglish
Pages (from-to)2388-2421
Number of pages34
JournalSIAM Journal on Optimization
Volume29
Issue number3
DOIs
Publication statusPublished - 24 Sep 2019

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