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Abstract
This paper discusses a kind of non-convex, non-smooth optimistic semivector bilevel optimization programs which equipped with a vector lower level problem. We introduce a class of new gap functions and penalty functions to transform this two level program into a one level scalar-objective optimization problem. Furthermore, we derive first-order optimality conditions for this semivector bilevel program in both global and local sense, using calculus of basic subdifferential and partial calmness. By applying new developments in basic subdifferential, we estimate basic subdifferential of gap functions and penalty functions which specify the former mentioned optimality conditions.
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