@inbook{9b1d959a21bc43f29c7db85a4fd42ca4,
title = "Scalarization of Set-Valued Optimization Problems in Normed Spaces",
abstract = "This work focuses on scalarization processes for nonconvex set-valued optimization problems whose solutions are defined by the socalled l-type less order relation, the final space is normed and the ordering cone is not necessarily solid. A scalarization mapping is introduced, which generalizes the well-known oriented distance, and its main properties are stated. In particular, by choosing a suitable norm it is shown that it coincides with the generalization of the so-called Tammer-Weidner nonlinear separation mapping to this kind of optimization problems. After that, two concepts of solution are characterized in terms of solutions of associated scalar optimization problems defined through the new scalarization mapping.",
keywords = "L-type less order relatio, Minimal solution, Optimality conditions, Oriented distance, Scalarization, Set-valued optimization, Strict minimal solution, L-type less order relatio, Minimal solution, Optimality conditions, Oriented distance, Scalarization, Set-valued optimization, Strict minimal solution",
author = "C{\'e}sar Guti{\'e}rrez and Bienvenido Jim{\'e}nez and Enrico Miglierina and Elena Molho",
year = "2015",
doi = "10.1007/978-3-319-18161-5\_43",
language = "English",
isbn = "978-3-319-18160-8",
volume = "359",
series = "ADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING",
pages = "505--512",
editor = "Le, \{Thi Hoai An\} and Pham, \{Dinh Tao\} and Nguyen, \{Ngoc Thanh\}",
booktitle = "Modelling, Computation and Optimization in Information Systems and Management Sciences",
}