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计算数学（英文版）
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2026年6期
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A FASTER PROXIMAL-INDEFINITE AUGMENTED LAGRANGIAN METHOD WITH O(1/k2)CONVERGENCE RATE
A FASTER PROXIMAL-INDEFINITE AUGMENTED LAGRANGIAN METHOD WITH O(1/k2)CONVERGENCE RATE
摘要
The augmented Lagrangian method(ALM),firstly proposed in 1969,remains a vital framework in large-scale constrained optimization.This paper addresses a linearly con-strained composite convex minimization problem and presents a general proximal ALM that incorporates both Nesterov acceleration and relaxed acceleration,while enjoying a proximal-indefinite term.Under mild assumptions without requiring prior knowledge of the objective function's strong convexity modulus,we establish the global convergence of the proposed method and derive an O(1/k2)nonergodic convergence rate for the La-grangian residual,the objective gap,and the constraint violation,where k denotes the iteration number.Numerical experiments on testing large-scale sparse signal reconstruc-tion tasks demonstrate the method's superior performance against several well-established methods.
年，卷(期)：
2026, 44(6)
分类号：
65Y20
90C25
机标分类号：
O236
TP273
G21
在线出版日期：
2026年9月15日
