On the completeness and constructiveness of parametric characterizations to vector optimization problems

SummaryMotivated by recent reviews of characterizations of optimal solutions to vector optimization problems and by applications to decision support systems, this paper presents a methodological approach to comparing such characterizations. After specifying attributes of constructiveness, alternative classes of characterizations are reviewed. Characterization theorems are quoted or presented in more detail in cases that supplement those given in recent reviews. One of alternative classes of characterizations — by aspiration levels and order-consistent achievement functions — is discussed in more detail. An impossibility theorem of complete and robustly computable characterization of efficient (as opposed to weakly or properly efficient) solutions to vector optimization problems is presented.ZusammenfassungAngeregt durch neuere Übersichten der Charakterisierung von optimalen Lösungen von Vektoroptimierungsproblemen und durch Anwendungen auf Entscheidungsunterstützungssysteme wird in diesem Beitrag ein methodischer Ansatz zum Vergleich solcher Charakterisierungen dargestellt. Nach der Spezifizierung von Attributen der Konstruktivität werden alternative Klassen von Charakterisierungen betrachtet. Charakterisierungstheoreme werden entweder zitiert oder, in Ergänzung neuerer Übersichten, dargestellt. Eine der alternativen Klassen der Charakterisierungen wird näher diskutiert. Ein Unmöglichkeitstheorem einer vollständigen und robust berechenbaren Charakterisierung von effizienten (im Gegensatz zu schwach oder streng effizienten) Lösungen der Vektoroptimierungsprobleme wird dargelegt.

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