Nonlinear separation in the image space with applications to constrained optimization. (English) Zbl 1386.90113
Summary: In this paper, by means of the image space analysis, we obtain optimality conditions for vector optimization of objective multifunction with multivalued constraints based on disjunction of two suitable subsets of the image space. By the oriented distance function a nonlinear regular separation is introduced and some optimality conditions for the constrained extremum problem are obtained. It is shown that the existence of a nonlinear separation is equivalent to a saddle point condition for the generalized Lagrangian function.
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 90C29 | Multi-objective and goal programming |
| 26B25 | Convexity of real functions of several variables, generalizations |
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