Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ ...Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.展开更多
针对径向基函数插值方法,提出了一种新的重启动策略来改进径向基的优化效果.在采用SLHD(symmetry Latin Hypercube design,对称拉丁超立方设计)方法换新的初始点对优化效果没有太大改进的时候,提出了一种更换径向基函数的重启动策略,可...针对径向基函数插值方法,提出了一种新的重启动策略来改进径向基的优化效果.在采用SLHD(symmetry Latin Hypercube design,对称拉丁超立方设计)方法换新的初始点对优化效果没有太大改进的时候,提出了一种更换径向基函数的重启动策略,可以取得更好的优化效果.通过数值算例说明了采用这种新的重启动策略在迭代次数上的优越性.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)
文摘Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.
文摘针对径向基函数插值方法,提出了一种新的重启动策略来改进径向基的优化效果.在采用SLHD(symmetry Latin Hypercube design,对称拉丁超立方设计)方法换新的初始点对优化效果没有太大改进的时候,提出了一种更换径向基函数的重启动策略,可以取得更好的优化效果.通过数值算例说明了采用这种新的重启动策略在迭代次数上的优越性.