论文标题
稀疏的优化问题以分数顺序Sobolev空间
Sparse optimization problems in fractional order Sobolev spaces
论文作者
论文摘要
我们考虑分数订单中的优化问题Sobolev Spaces $ H^s（ω）$，$ s \ in（0,1）$，稀疏促进了包含$ l^p $ -pseudonorms的目标函数，$ p \ in（0,1）$。证明了解决方案的存在。通过平滑方案，我们获得一阶最佳条件。开发了基于此平滑方案的算法。迭代液的弱限点显示出比必要条件给出的平稳性系统略有弱的平稳性系统。
We consider optimization problems in the fractional order Sobolev spaces $H^s(Ω)$, $s\in (0,1)$, with sparsity promoting objective functionals containing $L^p$-pseudonorms, $p\in (0,1)$. Existence of solutions is proven. By means of a smoothing scheme, we obtain first-order optimality conditions. An algorithm based on this smoothing scheme is developed. Weak limit points of iterates are shown to satisfy a stationarity system that is slightly weaker than that given by the necessary condition.
