2017/03/01 by Hong‐Kun Xu · 1 citation
Mathematics · Engineering · Computer Science · #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Optimization and Variational Analysis
paper · doi:10.1088/1361-6420/33/4/044008
openalex publication_date 2017/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/28
Abstract Bounded perturbation resilience and superiorization techniques for the projected scaled gradient (PSG) method are studied under the general Hilbert space setting. Weak convergence results of the (superiorized) PSG method and its relaxed version are proved under the assumption that the errors be summable. It is also shown that the PSG method converges in a sublinear rate and can be accelerated to the convergence rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:mrow> </mml:mfenced> </mml:math> . Applications to linear inverse problems and split feasibility problems are discussed.