论文标题
最佳条件和Lagrange乘数用于形状和拓扑优化问题
Optimality conditions and Lagrange multipliers for shape and topology optimization problems
论文作者
论文摘要
我们讨论了针对Neumann边界条件和边界观察的几何优化问题的一阶最佳条件。我们在这里开发的方法适用于大型的状态系统或成本功能。我们的方法基于隐式参数化定理和哈密顿系统的使用。它建立了有限的最佳控制问题的等效性，并在新的简单约束资格下使用Lagrange乘数。在这种情况下，进行一般功能变化，以自然方式结合拓扑和边界变化。
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals. Our approach is based on the implicit parametrization theorem and the use of Hamiltonian systems. It establishes equivalence with a constrained optimal control problem and uses Lagrange multipliers under a new simple constraint qualification. In this setting, general functional variations are performed, that combine topological and boundary variations in a natural way.
