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This chapter considers an optimal control problem with a semilinear state equation. For simplicity, we choose a quadratic cost functional as in Chap. 4 or Chap. 5 . Pointwise inequality constraints on the control variable, as in Chap. 5 , are also included. We discuss necessary and sufficient optimality conditions for this class of problems and present numerical analysis based on second-order sufficient optimality conditions.

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Semilinear State Equation

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  • 发表日期：

    2025年

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  • Boris Vexler,
  • Dominik Meidner

摘要

This chapter considers an optimal control problem with a semilinear state equation. For simplicity, we choose a quadratic cost functional as in Chap. 4 or Chap. 5 . Pointwise inequality constraints on the control variable, as in Chap. 5 , are also included. We discuss necessary and sufficient optimality conditions for this class of problems and present numerical analysis based on second-order sufficient optimality conditions.