It is prominent that conjugate gradient method is a high-efficient solution way for large-scale optimization problems.However,most of the conjugate gradient methods do not have sufficient descent property.In this pape...It is prominent that conjugate gradient method is a high-efficient solution way for large-scale optimization problems.However,most of the conjugate gradient methods do not have sufficient descent property.In this paper,without any line search,the presented method can generate sufficient descent directions and trust region property.While use some suitable conditions,the global convergence of the method is established with Armijo line search.Moreover,we study the proposed method for solving nonsmooth problems and establish its global convergence.The experiments show that the presented method can be applied to solve smooth and nonsmooth unconstrained problems,image restoration problems and Muskingum model successfully.展开更多
针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化...针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。展开更多
基金supported by the National Natural Science Foundation of China(No.11661009)the High Level Innovation Teams and Excellent Scholars Program in Guangxi institutions of higher education(No.[2019]52)+2 种基金the Guangxi Natural Science Key Fund(No.2017GXNSFDA198046)the Special Funds for Local Science and Technology Development Guided by the Central Government(No.ZY20198003)the special foundation for Guangxi Ba Gui Scholars.
文摘It is prominent that conjugate gradient method is a high-efficient solution way for large-scale optimization problems.However,most of the conjugate gradient methods do not have sufficient descent property.In this paper,without any line search,the presented method can generate sufficient descent directions and trust region property.While use some suitable conditions,the global convergence of the method is established with Armijo line search.Moreover,we study the proposed method for solving nonsmooth problems and establish its global convergence.The experiments show that the presented method can be applied to solve smooth and nonsmooth unconstrained problems,image restoration problems and Muskingum model successfully.
文摘针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。
