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

doi:10.15960/j.cnki.issn.1007-6093.2017.01.011

Abstract

Abstract:

The augmented Lagrange method is an effective method for solving nonlinear optimization problems. This paper, from a new pointview, studies the convergence of the augmented Lagrange method for the nonlinear nonsmooth convex programming problem with inequality constraints. The convergence of the gradient method with constant stepsize for the dual problem, based on the augmented Lagrange function, is demonstrated by using a convergence theorem of a gradient method with constant stepsize, from which the global convergence of the multiplier iteration of augmented Lagrange method is obtained.

Key words: gradient method, Moreau envelope, augmented Lagrangian dual, global convergence

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TIAN Zhaowei, ZHANG Liwei. A look at the convergence of the augmented Lagrange method for nondifferentiable convex programming from the view of a gradient method with constant stepsize[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.01.011.

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A look at the convergence of the augmented Lagrange method for nondifferentiable convex programming from the view of a gradient method with constant stepsize

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