Sensitivity Analysis Of Approximate Penalty In Banach Spaces

In this paper,we use the smoothed penalty term to approximated the non-smooth penalty term,and study the sensitivity of the Tikhonov functional approximation penalty in Banach space.Based on the classical Tikhonov functional,we use the p-frame and the Kadec-Klee property of the separable Banach space to analyze the sensitivity of a class of separable terms.It is proved that the minimally ordered sequence of separable approximate functional converges to the original the minimal element of the function.This paper first introduces the development of nonlinear ill-posed problem,sensitivity analysis and sparse constraint regularization,as well as the background and significance of this paper,and briefly introduces the main work of this paper.Secondly,we give the definition of Tikhonov functional approximation penalty in Banach space and its properties and theorems in inverse problem.Then we use the generalized discrepancy principle in posterior strategy to select the regularization parameter,and analyze the sensitivity of the Tikhonov functional penalty with parameters.Then we introduce the relationship between weak convergence and strong convergence.Finally,the Kadec-Klee property of the space is extended to the Kadec-Klee property of the functional sequence.Finally,we introduce the definition and properties of the p-frame of separable Banach spaces,and discuss the sensitivity of a class of separable penalty approximation by using the p-frame and the Kadec-Klee property of the separable Banach space.It is proved that the minimal element sequence of the approximate functional converge to the minimal element of the original functional.Finally,an example is given to show the effectiveness of the smooth penalty term near the non-smooth penalty method.