Optimality conditions for vector optimization problems with non-cone constraints in image space. (English) Zbl 1433.49034
Summary: In this paper, we employ the image space analysis method to investigate a vector optimization problem with non-cone constraints. First, we use the linear and nonlinear separation techniques to establish Lagrange-type sufficient and necessary optimality conditions of the given problem under convexity assumptions and generalized Slater condition. Moreover, we give some characterizations of generalized Lagrange saddle points in image space without any convexity assumptions. Finally, we derive the vectorial penalization for the vector optimization problem with non-cone constraints by a general way.
MSC:
| 49K27 | Optimality conditions for problems in abstract spaces |
| 90C46 | Optimality conditions and duality in mathematical programming |
Keywords:
nonlinear scalarization function; separation function; Lagrange-type optimality condition; penalizationReferences:
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