eprintid: 14142
rev_number: 6
eprint_status: archive
userid: 5
dir: disk0/00/01/41/42
datestamp: 2016-12-14 08:45:17
lastmod: 2021-08-27 17:28:16
status_changed: 2016-12-14 08:45:17
type: book_section
metadata_visibility: show
item_issues_count: 2
creators_name: Valyi, I.
creators_id: AL1323
title: Epsilon Solutions and Duality in Vector Optimization
ispublished: pub
divisions: prog_sds
abstract: The study of epsilon solutions in vector optimization problems was started in 1979 by S. S. Kutateladze [1]. These types of solutions are interesting because of their relation to non-differentiable optimization and the vector valued extensions of Ekeland’s variational principle as considered by P. Loridan [2] and I. Vályi [3], but computational aspects are perhaps even more important. In practical situations, namely, we often stop the calculations at values that we consider sufficiently close to the optimal solution, or use algorithms that result in some approximates of the Pareto set. Such procedures can result in epsilon solutions that are under study in this paper. A paper by D. J. White [4] deals with this issue and investigates how well these solutions approximate the exact solutions.
date: 1987
date_type: published
publisher: Springer Berlin Heidelberg
id_number: 10.1007/978-3-642-46607-6_45
creators_browse_id: 2471
creators_browse_id: 2643
creators_browse_id: 2222
full_text_status: none
series: Lecture Notes in Economics and Mathematical Systems
volume: 285
place_of_pub: Germany
pagerange: 417-426
refereed: TRUE
isbn: 978-3-642-46607-6
issn: 0075-8442
book_title: Toward Interactive and Intelligent Decision Support Systems
editors_name: Sawaragi, Y.
editors_name: Inoue, K.
editors_name: Nakayama, H.
editors_id: AL1624
editors_id: AL0282
coversheets_dirty: FALSE
fp7_type: info:eu-repo/semantics/bookPart
citation:   Valyi, I. <https://pure.iiasa.ac.at/view/iiasa/2471.html>  (1987).  Epsilon Solutions and Duality in Vector Optimization.    In:  Toward Interactive and Intelligent Decision Support Systems. Eds. Sawaragi, Y. <https://pure.iiasa.ac.at/view/iiasa/2643.html>, Inoue, K., & Nakayama, H. <https://pure.iiasa.ac.at/view/iiasa/2222.html>, pp. 417-426 Germany: Springer Berlin Heidelberg.  ISBN 978-3-642-46607-6 10.1007/978-3-642-46607-6_45 <https://doi.org/10.1007/978-3-642-46607-6_45>.