On approximate efficiency for nonsmooth robust vector optimization problems. (English) Zbl 1499.90190
Summary: In this article, we use the robust optimization approach (also called the worst-case approach) for finding \(\epsilon\)-efficient solutions of the robust multiobjective optimization problem defined as a robust (worst-case) counterpart for the considered nonsmooth multiobjective programming problem with the uncertainty in both the objective and constraint functions. Namely, we establish both necessary and sufficient optimality conditions for a feasible solution to be an \(\epsilon\)-efficient solution (an approximate efficient solution) of the considered robust multiobjective optimization problem. We also use a scalarizing method in proving these optimality conditions.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C17 | Robustness in mathematical programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C30 | Nonlinear programming |
Keywords:
robust optimization approach; robust multiobjective optimization; \(\epsilon\)-efficient solution; \(\epsilon\)-optimality conditions; scalarizationReferences:
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