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http://hdl.handle.net/10397/93289
Title: | Fully piecewise linear vector optimization problems | Authors: | Zheng, XY Yang, X |
Issue Date: | Aug-2021 | Source: | Journal of optimization theory and applications, Aug. 2021, v. 190, no. 2, p. 461-490 | Abstract: | We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector optimization problem with the objective and constraint functions being piecewise linear. To solve this problem, we divide it into some linear subproblems and structure a dimensional reduction method. Under some mild assumptions, we prove that its Pareto (resp., weak Pareto) solution set is the union of finitely many generalized polyhedra (resp., polyhedra), each of which is contained in a Pareto (resp., weak Pareto) face of some linear subproblem. Our main results are even new in the linear case and further generalize Arrow, Barankin and Blackwell’s classical results on linear vector optimization problems in the framework of finite-dimensional spaces. | Keywords: | Pareto solution Piecewise linear function Polyhedron Weak Pareto solution |
Publisher: | Springer | Journal: | Journal of optimization theory and applications | ISSN: | 0022-3239 | EISSN: | 1573-2878 | DOI: | 10.1007/s10957-021-01889-w | Rights: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use(https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10957-021-01889-w |
Appears in Collections: | Journal/Magazine Article |
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Yang_Fully_Piecewise_Linear.pdf | Pre-Published version | 242.12 kB | Adobe PDF | View/Open |
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