Minimax Theory and its Applications 09 (2024), No. 2, 325--339
Copyright Heldermann Verlag 2024
Connectedness in Set Optimization via a Nonlinear Scalarization
Bienvenido Jiménez
Departamento de Matemática Aplicada, E.T.S. de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, Madrid, Spain
bjimenez@ind.uned.es
We consider the sets of minimal solutions and weak minimal solutions to a set optimization problem with respect to the lower and upper set less relations. Via a nonlinear scalarization based on the oriented distance, we establish that they are connected under the assumption of strictly natural quasi cone-convexity.
Keywords: Set optimization, connectedness, weak l-minimal solution, lower set less relation, scalarization.
MSC: 49J53, 90C29.
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