Optimality conditions for weak efficiency in vector optimisation using vectorial penalisation
Optimization Eruditorum, Volume 4, Issue 1, April 2027, Pages 88–106
Christian Günther
Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany
Elisabeth Köbis
Department of Mathematics, Norwegian University of Science and Technology, Alfred Getz’ vei 1, Trondheim, 7034, Norway
Paul Schmölling
Department of Mathematics, Norwegian University of Science and Technology, Alfred Getz’ vei 1, Trondheim, 7034, Norway
Christiane Tammer
Faculty of Natural Sciences II, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Theodor-Lieser-Straße 5, Halle (Saale), 06120, Germany
Abstract
We establish necessary optimality conditions for weakly efficient solutions of constrained, potentially nonconvex vector optimisation problems. The conditions are obtained by combining an unconstrained reformulation based on vectorial penalisation with nonlinear scalarisation and abstract subdifferential rules. Explicit multiplier conditions are derived for single and finite inequality systems, equality and mixed constraints, and closed convex feasible sets.
Cite this Article as
Christian Günther, Elisabeth Köbis, Paul Schmölling, and Christiane Tammer, Optimality conditions for weak efficiency in vector optimisation using vectorial penalisation, Optimization Eruditorum, 4(1), 88–106, 2027