论文标题
一类平等限制的最佳价值功能的一阶可不同性属性与应用程序
First-order differentiability properties of a class of equality constrained optimal value functions with applications
论文作者
论文摘要
在本文中，我们研究了参数imimum函数的正确可不同性，而不是由平等约束定义的参数集。我们提出了一个新定理，该定理具有足够的条件，可与参数相对于参数。目标应用程序是在最佳控制和形状优化中产生的非凸目标函数。该定理与Kunisch，ITO和PEICHL的各种方法结合使用了平均的伴随方法。我们提供了两个抽象结果的示例：（a）涉及半连接部分微分方程的形状优化问题，该方程表现出无限的许多解决方案，（b）受非线性方程式的有限维二次函数。
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to the parameter. Target applications are nonconvex objective functions with equality constraints arising in optimal control and shape optimisation. The theorem makes use of the averaged adjoint approach in conjunction with the variational approach of Kunisch, Ito and Peichl. We provide two examples of our abstract result: (a) a shape optimisation problem involving a semilinear partial differential equation which exhibits infinitely many solutions, (b) a finite dimensional quadratic function subject to a nonlinear equation.
