In this paper, we deal with the existence and multiplicity of solutions to the frac- tional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation...In this paper, we deal with the existence and multiplicity of solutions to the frac- tional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that our problem has at least three solutions.展开更多
In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both cons...In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.展开更多
We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite terminat...We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite termination technique, is bounded above by O( n1.5). The random LP problem is Todd’s probabilistic model with the standard Gauss distribution.展开更多
基金Supported by NSFC(11371282,11201196)Natural Science Foundation of Jiangxi(20142BAB211002)
文摘In this paper, we deal with the existence and multiplicity of solutions to the frac- tional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that our problem has at least three solutions.
基金supported by the Zhejiang Provincial Natural Science Foundation of China under grant No.LQ21A010003.
文摘In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.
文摘We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite termination technique, is bounded above by O( n1.5). The random LP problem is Todd’s probabilistic model with the standard Gauss distribution.
