从常步长梯度方法的视角看不可微凸优化增广Lagrange方法的收敛性
发布时间：2018-09-04 17:00
【摘要】：增广Lagrange方法是求解非线性规划的一种有效方法.从一新的角度证明不等式约束非线性非光滑凸优化问题的增广Lagrange方法的收敛性.用常步长梯度法的收敛性定理证明基于增广Lagrange函数的对偶问题的常步长梯度方法的收敛性,由此得到增广Lagrange方法乘子迭代的全局收敛性.
[Abstract]:The augmented Lagrange method is an effective method for solving nonlinear programming. The convergence of the augmented Lagrange method for inequality constrained nonlinear nonsmooth convex optimization problems is proved from a new point of view. By using the convergence theorem of the constant step size gradient method, the convergence of the constant step size gradient method based on the dual problem of augmented Lagrange function is proved, and the global convergence of the multiplier iteration of the augmented Lagrange method is obtained.
【作者单位】： 华侨大学数学科学学院;
【基金】：国家自然科学基金(Nos.91330206,11571059) 福建省中青年教师教育科研项目(No.JAT160024)
【分类号】：O224
，
本文编号：2222795
[Abstract]:The augmented Lagrange method is an effective method for solving nonlinear programming. The convergence of the augmented Lagrange method for inequality constrained nonlinear nonsmooth convex optimization problems is proved from a new point of view. By using the convergence theorem of the constant step size gradient method, the convergence of the constant step size gradient method based on the dual problem of augmented Lagrange function is proved, and the global convergence of the multiplier iteration of the augmented Lagrange method is obtained.
【作者单位】： 华侨大学数学科学学院;
【基金】：国家自然科学基金(Nos.91330206,11571059) 福建省中青年教师教育科研项目(No.JAT160024)
【分类号】：O224
，
本文编号：2222795
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