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Title: Existence of efficient and properly efficient solutions to problems of constrained vector optimization
Authors: Kim, Do Sang
Mordukhovich, Boris S.
Phạm, Tiến Sơn 
Nguyen, Van Tuyen
Keywords: Existence theorems;Pareto efficient solutions;Geoffrion-properly efficient solutions;M-tameness;Palais–Smale conditions;Properness
Issue Date: 2020
Publisher: SpringerLink
Journal: Mathematical Programming 
The paper is devoted to the existence of global optimal solutions for a general class of
nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint set. The main attention is paid to the two major notions of optimality
in vector problems: Pareto efficiency and proper efficiency in the sense of Geoffrion.
Employing adequate tools of variational analysis and generalized differentiation, we
first establish relationships between the notions of properness, M-tameness, and the
Palais–Smale conditions formulated for the restriction of the vector cost mapping on
the constraint set. These results are instrumental to derive verifiable necessary and sufficient conditions for the existence of Pareto efficient solutions in vector optimization.
Furthermore, the developed approach allows us to obtain new sufficient conditions
for the existence of Geoffrion-properly efficient solutions to such constrained vector
DOI: 10.1007/s10107-020-01532-y
Type: Bài báo đăng trên tạp chí thuộc ISI, bao gồm book chapter
Appears in Collections:Tạp chí (Khoa Toán - Tin học)

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