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Improvement sets and vector optimization
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DOI：10.1016/j.ejor.2012.05.050.png)
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Abstract
En 中文
In this paper we focus oil minimal points in linear spaces and minimal solutions of vector optimization problems, where the preference relation is defined via an improvement set E. To be precise, we extend the notion of E-optimal point due to Chicco et al. in [4] to a general (non-necessarily Pareto) quasi ordered linear space and we study its properties. In particular, we relate the notion of improvement set with other similar concepts of the literature and we characterize it by means of sublevel sets of scalar functions. Moreover, we obtain necessary and sufficient conditions for E-optimal solutions of vector optimization problems through scalarization processes by assuming convexity assumptions and also in the general (nonconvex) case. By applying the obtained results to certain improvement sets we generalize well-known results of the literature referred to efficient, weak efficient and approximate efficient solutions of vector optimization problems. (C) 2012 Elsevier B.V. All rights reserved.
Keywords:
Improvement set
Minimal point
Vector optimization
epsilon-Efficiency
Scalarization
Journal
IF:
6
Papers:
2.2W
Citations:
6.4W