An Augmented Lagrangian Method for
An Augmented Lagrangian Method for
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DOI：
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发表时间：
2010
影响因子：
2
通讯作者：
J. Koko;Stéphanie Jehan-Besson-
中科院分区：
文献类型：
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作者：
J. Koko;Stéphanie Jehan-Besson-
其中松弛变量si ≥ 0。我们使用它（为什么？）si = 0或si = ci − μλi。定理设x ∈ R是具有等式约束的完全问题的局部解（为简单起见）.设LICQ和二阶充分条件对λ = λ满足。然后有一个阈值μ ∈（0，μ ∈]，x ∈是LA的严格局部极小。证明目标是证明对于u ∈ Rn，u <$xxLA = 0，且u <$xxLAu > 0。由于ci（x）= 0，第一个KKT条件是显而易见的：对于任何μ
with slack variables si ≥ 0. We use that (why?) si = 0 or si = ci − μλi . Theorem Let x∗ be a local solution of the full problem with equality constraints (for simplicity). Suppose LICQ and second-order sufficient conditions are satisfied for λ = λ∗. Then there is a threshhold μ̄ such that for any μ ∈ (0, μ̄], x∗ is a strict local minimizer of LA. Proof Goal is to show ∇xLA = 0, and u∇xxLAu > 0 for u ∈ Rn. Since ci(x) = 0, the first KKT condition is obvious: for any μ