Vector variational inequality with pseudoconvexity on Hadamard manifolds. (English) Zbl 1377.90084
The authors consider vector optimization and vector variational inequality problems on Hadamard manifolds. It is known that the scalar variational inequality serves as necessary optimality condition for the usual optimization problem and that they are equivalent if the cost function is pseudoconvex. Besides, these properties are extended for the usual and weak vector problems. The paper contains further extensions of these and some related properties for the case of vector problems on Hadamard manifolds with proper adjustment of the concepts.
Reviewer: Igor V. Konnov (Kazan)
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 58E35 | Variational inequalities (global problems) in infinite-dimensional spaces |
Keywords:
Hadamard manifolds; pseudoconvex functions; vector variational inequality; vector optimization problemReferences:
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