Sparse optimization problems in fractional order Sobolev spaces. (1st April 2023)

• Record Type: Journal Article
• Authors: Antil, Harbir; Wachsmuth, Daniel
• Is Part Of: Inverse problems. Volume 39:Number 4(2023)
• Publication Date: 2023-04-01
• Subjects: fractional Sobolev space -- sparse optimization -- Lp functionals -- necessary optimality conditions; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/acbe5e
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider optimization problems in the fractional order Sobolev spaces with sparsity promoting objective functionals containing L p -pseudonorms, p ∈ ( 0, 1 ) . Existence of solutions is proven. By means of a smoothing scheme, we obtain first-order optimality conditions, which contain an equation with the fractional Laplace operator. 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.