Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure
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In this paper, we introduce Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure. We prove the connections between Benson properly nondominated, Hartley properly nondominated, and super nondominated solutions under appropriate assumptions. Moreover, we establish some necessary and sufficient conditions for newly-defined solutions invoking an augmented dual cone approach, the linear scalarization, and variational analysis tools. In addition to the theoretical results, various clarifying examples are given.
KeywordsVector optimization Variable ordering structure (VOS) Properly nondominated solution Super nondominated solution Augmented dual cone Linear scalarization Variational analysis
The authors would like to express their gratitude to two anonymous referees and the associate editor for their helpful comments on the earlier versions of the paper. The research of the second author was in part supported by a grant from the Iran National Science Foundation (INSF) (No. 95849588).
- 11.Eichfelder, G.: Vector optimization in medical engineering, In: Pardalos, P.M., Rassias T.M. (eds.) Mathematics Without Boundaries, pp. 181–215. Springer, New York (2014)Google Scholar
- 25.Kuhn, H., Tucker, A.: Nonlinear programming. In: Neyman, J. (ed.) Proceeding of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. University of California Press, Berkeley, California (1951)Google Scholar
- 27.Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory. Springer, Berlin (2006)Google Scholar