<p>In this paper, a nondifferentiable interval-valued bilevel optimization problem is considered in which the involved functions are characterized by their tangential subdifferentials. Optimality conditions are established for the aforesaid nonsmooth extremum problem in such a way that its hierarchical model is transformed into a single-level one using the optimal value reformulation. Under the nonsmooth Abadie constraint qualification, necessary optimality conditions of Karush-Kuhn-Tucker type are proved for the considered nondifferentiable interval-valued bilevel optimization problem in terms of tangential subdifferentials of the involved functions. Further, sufficient optimality conditions are also derived for this aforementioned nonsmooth extremum problem under assumptions that the functions constituting it are Dini generalized convex, characterized by their tangential subdifferentials. The optimality conditions established in the paper are illustrated by the examples of nondifferentiable interval-valued bilevel optimization problems.</p>

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Optimality Conditions for Nondifferentiable Interval-Valued Bilevel Optimization Problems via Tangential Subdifferentials

  • Tadeusz Antczak,
  • Rishabh Pandey,
  • Vinay Singh

摘要

In this paper, a nondifferentiable interval-valued bilevel optimization problem is considered in which the involved functions are characterized by their tangential subdifferentials. Optimality conditions are established for the aforesaid nonsmooth extremum problem in such a way that its hierarchical model is transformed into a single-level one using the optimal value reformulation. Under the nonsmooth Abadie constraint qualification, necessary optimality conditions of Karush-Kuhn-Tucker type are proved for the considered nondifferentiable interval-valued bilevel optimization problem in terms of tangential subdifferentials of the involved functions. Further, sufficient optimality conditions are also derived for this aforementioned nonsmooth extremum problem under assumptions that the functions constituting it are Dini generalized convex, characterized by their tangential subdifferentials. The optimality conditions established in the paper are illustrated by the examples of nondifferentiable interval-valued bilevel optimization problems.