基于无穷范数非光滑优化的光滑化方法-运筹学与控制论专业论文.docxVIP

基于无穷范数非光滑优化的光滑化方法 基于无穷范数非光滑优化的光滑化方法 万方数据 万方数据 万方数据 万方数据 II Smoothing Smoothing Methods for Optimization Problem B ased on粤。o Minimizat ion Abstract It has wide range of applications for solving the underdetermined system of linear equ孙 tions in the field of image restoration and reconstruction，and it has drawn lncreasmg attentlon from scholars recent years．There many important results about solving underdetermmed linear svstem of equations problem，however，we don’t much deep study on methods tor underdetemined system of linear equations based on孽。。optimization problem·Therefore，this paper focuses on study of the smoothing methods of nonsmooth optimization based on掣 op。 timization problem，namely the original problem is transformed to its smoothing approⅪmate problem by smoothing孽。0 through the entropy function to solve- Firstly,the development and status quo of image reconstruction technology and the metn’ ods of solving the nonsmooth optimization problems briefly introduced．Then we introduce the smoothing method and show that the difference between the optimal values of the ongmaI function and the approximate one．We will research俨minimization optimization Problem mln ll让llo。 uER” s．t． Au=d， where乱∈形indicated the reconstructed image，A∈Rm姗indicated the sensor matrix，d∈Rm indicated the observed data． GeneraIIy，we translate粤o。minimization optimization problem into Z2一粤oo minimization optimization problem to solve，that is 牡m∈Rin。lI让Il。。+会11A札一dll；， where入∈ (0，+∞)，we will convert the optimization problem into its smoothing approxim砒ion problem mln 日(u) =弘ln[∑(e警 +e一警)]+害IIA“一dIl；， uER” i=1 order to accel- it be solved by using the improved split Bregman iterative algorithm·In erate the algorithm，we add the iterations of the smoothing parameter p to Bregman 1teratlve solutlons wnlcn algorithm．and prove the convergence of the algorithm，that is，a sequence of is generated by the algorithm converges to the optimal solution of the original optimizatlon Droblem in limited itera