<p>In this paper, we investigate a nonsmooth multiobjective bilevel optimal control problem with pure state constraints. The functions involved are not necessarily continuously differentiable, and we do not assume that either the objective function or the constraint functions of the lower-level optimization problem are convex with respect to all variables. By employing variational analysis techniques along with a weakened version of the Mangasarian–Fromovitz constraint qualification, we derive the necessary optimality conditions for a local efficient solution in terms on limiting normal cones and limiting subdifferentials. For the smooth case, we derive detailed optimality conditions using Mordukhovich’s generalized differentiation calculus. We also provide an example that illustrates our findings and highlights the limitations of certain previous studies.</p>

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On Weakened MFCQ for a Specific Multiobjective Bilevel Optimal Control Problem

  • Nazih Abderrazzak Gadhi

摘要

In this paper, we investigate a nonsmooth multiobjective bilevel optimal control problem with pure state constraints. The functions involved are not necessarily continuously differentiable, and we do not assume that either the objective function or the constraint functions of the lower-level optimization problem are convex with respect to all variables. By employing variational analysis techniques along with a weakened version of the Mangasarian–Fromovitz constraint qualification, we derive the necessary optimality conditions for a local efficient solution in terms on limiting normal cones and limiting subdifferentials. For the smooth case, we derive detailed optimality conditions using Mordukhovich’s generalized differentiation calculus. We also provide an example that illustrates our findings and highlights the limitations of certain previous studies.