Abstract
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.
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Acknowledgments
The authors are very grateful to the referees for their constructive comments, specially for having suggested the comparison of the data qualifications used in this paper with the regularity conditions recently introduced in [17].
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This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P.
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Goberna, M.A., Kanzi, N. Optimality conditions in convex multiobjective SIP. Math. Program. 164, 167–191 (2017). https://doi.org/10.1007/s10107-016-1081-8
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DOI: https://doi.org/10.1007/s10107-016-1081-8