The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces....The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.展开更多
针对非光滑非凸–强拟凹鞍点问题,本文利用Bregman距离建立了Bregman近端梯度上升下降算法。对Bregman近端梯度上升迭代算法中,得到内部最大化问题函数差值不等式,从而得到近端梯度上升迭代点之间的不等式关系。对于非凸非光滑问题,引...针对非光滑非凸–强拟凹鞍点问题,本文利用Bregman距离建立了Bregman近端梯度上升下降算法。对Bregman近端梯度上升迭代算法中,得到内部最大化问题函数差值不等式,从而得到近端梯度上升迭代点之间的不等式关系。对于非凸非光滑问题,引入扰动类梯度下降序列,得到算法的次收敛性,当目标函数为半代数时,得到算法的全局收敛性。For the nonsmooth nonconvex-strongly quasi-concave saddle point problems, this paper establishes the Bregman proximal gradient ascent-descent algorithm by using the Bregman distance. In the Bregman proximal gradient ascent iterative algorithm, the difference inequality of the internal maximization problem function is obtained, and thus the inequality relationship between the proxi-mal gradient ascent iterative points is derived. For nonconvex and nonsmooth problems, a perturbed gradient-like descent sequence is introduced to obtain the sub-convergence of the algorithm. When the objective function is semi-algebraic, the global convergence of the algorithm is obtained.展开更多
由于传统的欧式空间方法无法有效反映协方差矩阵之间的差异,而导致信息损失,为了解决这一问题,提出了一种基于詹森-布雷格曼洛格德特散度(Jensen-Bregman LogDet divergence)的阵列波达方向(Direction of Arrival,DOA)估计方法,将目标...由于传统的欧式空间方法无法有效反映协方差矩阵之间的差异,而导致信息损失,为了解决这一问题,提出了一种基于詹森-布雷格曼洛格德特散度(Jensen-Bregman LogDet divergence)的阵列波达方向(Direction of Arrival,DOA)估计方法,将目标方位估计问题转化为矩阵流形上两点间的几何距离问题,揭示了方位估计与黎曼空间矩阵流形的映射规律,从而得到了几何距离最小值处对应的角度即为目标入射角度的结论,并通过构建两个强鲁棒性的矩阵流形,完成了矩阵信息几何DOA估计理论模型的建立。通过模拟仿真与实测数据对所新方法进行了验证。验证结果表明:与现有的最小方差无失真响应算法和多信号分类算法相比,新方法在低信噪比环境下拥有更好的估计精度;新方法的应用具有一定的实际意义和应用前景,可以为海洋防御及民用领域中的水下目标方位估计等提供坚实的技术支持。展开更多
在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c...在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.展开更多
As a complement to X-ray computed tomography(CT),neutron tomography has been extensively used in nuclear engineer-ing,materials science,cultural heritage,and industrial applications.Reconstruction of the attenuation m...As a complement to X-ray computed tomography(CT),neutron tomography has been extensively used in nuclear engineer-ing,materials science,cultural heritage,and industrial applications.Reconstruction of the attenuation matrix for neutron tomography with a traditional analytical algorithm requires hundreds of projection views in the range of 0°to 180°and typically takes several hours to complete.Such a low time-resolved resolution degrades the quality of neutron imaging.Decreasing the number of projection acquisitions is an important approach to improve the time resolution of images;however,this requires efficient reconstruction algorithms.Therefore,sparse-view reconstruction algorithms in neutron tomography need to be investigated.In this study,we investigated the three-dimensional reconstruction algorithm for sparse-view neu-tron CT scans.To enhance the reconstructed image quality of neutron CT,we propose an algorithm that uses OS-SART to reconstruct images and a split Bregman to solve for the total variation(SBTV).A comparative analysis of the performances of each reconstruction algorithm was performed using simulated and actual experimental data.According to the analyzed results,OS-SART-SBTV is superior to the other algorithms in terms of denoising,suppressing artifacts,and preserving detailed structural information of images.展开更多
In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multiplie...In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.展开更多
基金Supported by NSFC(No.12171062)the Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-JQX0004)+1 种基金the Chongqing Talent Support Program(No.cstc2024ycjh-bgzxm0121)Science and Technology Project of Chongqing Education Committee(No.KJZD-M202300503)。
文摘The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.
文摘针对非光滑非凸–强拟凹鞍点问题,本文利用Bregman距离建立了Bregman近端梯度上升下降算法。对Bregman近端梯度上升迭代算法中,得到内部最大化问题函数差值不等式,从而得到近端梯度上升迭代点之间的不等式关系。对于非凸非光滑问题,引入扰动类梯度下降序列,得到算法的次收敛性,当目标函数为半代数时,得到算法的全局收敛性。For the nonsmooth nonconvex-strongly quasi-concave saddle point problems, this paper establishes the Bregman proximal gradient ascent-descent algorithm by using the Bregman distance. In the Bregman proximal gradient ascent iterative algorithm, the difference inequality of the internal maximization problem function is obtained, and thus the inequality relationship between the proxi-mal gradient ascent iterative points is derived. For nonconvex and nonsmooth problems, a perturbed gradient-like descent sequence is introduced to obtain the sub-convergence of the algorithm. When the objective function is semi-algebraic, the global convergence of the algorithm is obtained.
文摘由于传统的欧式空间方法无法有效反映协方差矩阵之间的差异,而导致信息损失,为了解决这一问题,提出了一种基于詹森-布雷格曼洛格德特散度(Jensen-Bregman LogDet divergence)的阵列波达方向(Direction of Arrival,DOA)估计方法,将目标方位估计问题转化为矩阵流形上两点间的几何距离问题,揭示了方位估计与黎曼空间矩阵流形的映射规律,从而得到了几何距离最小值处对应的角度即为目标入射角度的结论,并通过构建两个强鲁棒性的矩阵流形,完成了矩阵信息几何DOA估计理论模型的建立。通过模拟仿真与实测数据对所新方法进行了验证。验证结果表明:与现有的最小方差无失真响应算法和多信号分类算法相比,新方法在低信噪比环境下拥有更好的估计精度;新方法的应用具有一定的实际意义和应用前景,可以为海洋防御及民用领域中的水下目标方位估计等提供坚实的技术支持。
文摘在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.
基金supported by the National Key Research and Development Program of China(No.2022YFB1902700)the National Natural Science Foundation of China(No.11875129)+3 种基金the Fund of the State Key Laboratory of Intense Pulsed Radiation Simulation and Effect(No.SKLIPR1810)the Fund of Innovation Center of Radiation Application(No.KFZC2020020402)the Fund of the State Key Laboratory of Nuclear Physics and Technology,Peking University(No.NPT2020KFY08)the Joint Innovation Fund of China National Uranium Co.,Ltd.,State Key Laboratory of Nuclear Resources and Environment,East China University of Technology(No.2022NRE-LH-02).
文摘As a complement to X-ray computed tomography(CT),neutron tomography has been extensively used in nuclear engineer-ing,materials science,cultural heritage,and industrial applications.Reconstruction of the attenuation matrix for neutron tomography with a traditional analytical algorithm requires hundreds of projection views in the range of 0°to 180°and typically takes several hours to complete.Such a low time-resolved resolution degrades the quality of neutron imaging.Decreasing the number of projection acquisitions is an important approach to improve the time resolution of images;however,this requires efficient reconstruction algorithms.Therefore,sparse-view reconstruction algorithms in neutron tomography need to be investigated.In this study,we investigated the three-dimensional reconstruction algorithm for sparse-view neu-tron CT scans.To enhance the reconstructed image quality of neutron CT,we propose an algorithm that uses OS-SART to reconstruct images and a split Bregman to solve for the total variation(SBTV).A comparative analysis of the performances of each reconstruction algorithm was performed using simulated and actual experimental data.According to the analyzed results,OS-SART-SBTV is superior to the other algorithms in terms of denoising,suppressing artifacts,and preserving detailed structural information of images.
文摘In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.
