RT info:eu-repo/semantics/article
T1 On the existence of weak efficient solutions of nonconvex vector optimization problems
A1 Gutiérrez Vaquero, César
A1 López, Rubén
K1 Vector optimization
K1 Weak efficient solution
K1 Existence result
K1 Coercive vector-valued function
K1 Colevel set
K1 Level set
K1 Nonlinear scalarization
AB We study vector optimization problems with solid non-polyhedral convex ordering cones, without assuming any convexity or quasiconvexity assumption. We state a Weierstrass-type theorem and existence results for weak efficient solutions for coercive and noncoercive problems. Our approach is based on a new coercivity notion for vector valued functions, two realizations of the Gerstewitz scalarization function, asymptotic analysis and a regularization of the objective function. We define new boundedness and lower semicontinuity properties for vector-valued functions and study their properties. These new tools rely heavily on the solidness of the ordering cone through the notion of colevel and level sets. As a consequence of this approach, we improve various existence results from the literature, since weaker assumptions are required
PB Springer
SN 0022-3239
YR 2020
FD 2020
LK https://uvadoc.uva.es/handle/10324/74142
UL https://uvadoc.uva.es/handle/10324/74142
LA eng
NO Journal of Optimization Theory and Applications, 2020, vol. 185, n. 3 p. 880-902
NO Producción Científica
DS UVaDOC
RD 04-abr-2025