Existence of efficient and properly efficient solutions to problems of constrained vector optimization
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...
Đã lưu trong:
| Những tác giả chính: | , , , |
|---|---|
| Định dạng: | Journal article |
| Ngôn ngữ: | English |
| Được phát hành: |
SpringerLink
2021
|
| Những chủ đề: | |
| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/handle/123456789/501 |
| Các nhãn: |
Thêm thẻ
Không có thẻ, Là người đầu tiên thẻ bản ghi này!
|
| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
|---|
| id |
oai:scholar.dlu.edu.vn:123456789-501 |
|---|---|
| record_format |
dspace |
| spelling |
oai:scholar.dlu.edu.vn:123456789-5012023-11-08T15:50:25Z Existence of efficient and properly efficient solutions to problems of constrained vector optimization Kim, Do Sang Mordukhovich, Boris S. Phạm, Tiến Sơn Nguyen, Van Tuyen Existence theorems Pareto efficient solutions Geoffrion-properly efficient solutions M-tameness Palais–Smale conditions Properness 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 problems. 2021-08-23T08:33:25Z 2021-08-23T08:33:25Z 2021 Journal article Bài báo đăng trên tạp chí thuộc ISI, bao gồm book chapter https://scholar.dlu.edu.vn/handle/123456789/501 10.1007/s10107-020-01532-y en Mathematical Programming 10.1007/s10107-020-01532-y 0025-5610 SpringerLink |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Existence theorems Pareto efficient solutions Geoffrion-properly efficient solutions M-tameness Palais–Smale conditions Properness |
| spellingShingle |
Existence theorems Pareto efficient solutions Geoffrion-properly efficient solutions M-tameness Palais–Smale conditions Properness Kim, Do Sang Mordukhovich, Boris S. Phạm, Tiến Sơn Nguyen, Van Tuyen Existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| description |
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
problems. |
| format |
Journal article |
| author |
Kim, Do Sang Mordukhovich, Boris S. Phạm, Tiến Sơn Nguyen, Van Tuyen |
| author_facet |
Kim, Do Sang Mordukhovich, Boris S. Phạm, Tiến Sơn Nguyen, Van Tuyen |
| author_sort |
Kim, Do Sang |
| title |
Existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| title_short |
Existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| title_full |
Existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| title_fullStr |
Existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| title_full_unstemmed |
Existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| title_sort |
existence of efficient and properly efficient solutions to problems of constrained vector optimization |
| publisher |
SpringerLink |
| publishDate |
2021 |
| url |
https://scholar.dlu.edu.vn/handle/123456789/501 |
| _version_ |
1782581195368824832 |