Abstract
Given a semi-infinite multiobjective convex problem we introduce a data qualification that enables to characterize optimality in terms of Lagrange multipliers. We show that this condition characterizes the weak efficient solutions through the weak Karush-Kuhn-Tucker (KKT) condition, and identifies the proper efficient solutions through the strong KKT condition. We also address the question in relation to a gap function.
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Acknowledgements
This work has been supported by MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and SECTyP-UNCuyo, Argentina, Res. 3853/2016-R.
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Goberna, M.Á., Rodríguez, M.M.L., Vera de Serio, V.N. (2018). The LFM Data Qualification in Convex Multiobjective Semi-infinite Programming. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_77
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DOI: https://doi.org/10.1007/978-3-319-73848-2_77
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