Optimality conditions in quasidifferentiable vector optimization. (English) Zbl 1349.49017
Summary: In the paper, the quasidifferentiable vector optimization problem with the inequality constraints is considered. The Fritz John-type necessary optimality conditions and the Karush-Kuhn-Tucker-type necessary optimality conditions for a weak Pareto solution are derived for such a nonsmooth vector optimization problem. Further, the concept of an \(F\)-convex function with respect to a convex compact set is introduced. Then, the sufficient optimality conditions for a (weak) Pareto optimality of a feasible solution are established for the considered nonsmooth multiobjective optimization problem under assumptions that the involved functions are quasidifferentiable \(F\)-convex with respect to convex compact sets which are equal to Minkowski sum of their subdifferentials and superdifferentials at this point.
MSC:
| 49J52 | Nonsmooth analysis |
| 90C29 | Multi-objective and goal programming |
| 90C30 | Nonlinear programming |
| 90C26 | Nonconvex programming, global optimization |
Keywords:
quasidifferentiable multiobjective optimization problem; Fritz John-type necessary optimality conditions; Karush-Kuhn-Tucker-type necessary optimality conditions; Pareto optimality; quasidifferentiable \(F\)-convexity with respect to a convex compact setReferences:
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