RT Journal Article
T1 Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities
A1 Ruíz-Garzón, Gabriel
A1 Osuna-Gómez, Rafaela
A1 Rufián-Lizana, Antonio
A1 Hernández-Jiménez, Beatriz
K1 Generalized convexity
K1 Hadamard manifold
K1 Approximate efficient solution
K1 Stackelberg equilibrium point
AB This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated them with examples. We see the minimum requirements under which critical points, solutions of Stampacchia, and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we show an economical application, again using solutions of the variational problems to identify Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.
PB MPDI
YR 2020
FD 2020-12-10
LK https://hdl.handle.net/10433/19484
UL https://hdl.handle.net/10433/19484
LA en
NO Ruiz-Garzón, Gabriel, Rafaela Osuna-Gómez, Antonio Rufián-Lizana, and Beatriz Hernández-Jiménez. 2020. "Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities" Mathematics 8, no. 12: 2196. https://doi.org/10.3390/math8122196
NO Dpto. Economía, Métodos Cuantitativos e Hª Económica
DS RIO
RD May 9, 2026