Complexity of Proximal Augmented Lagrangian for Nonconvex Optimization with Nonlinear Equality Constraints
Complexity of Proximal Augmented Lagrangian for Nonconvex Optimization with Nonlinear Equality Constraints
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DOI：
10.1007/s10915-021-01409-y
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发表时间：
2019-07
影响因子：
2.5
通讯作者：
Yue Xie;Stephen J. Wright
中科院分区：
文献类型：
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作者：
Yue Xie;Stephen J. Wright
我们分析了最坏情况下的非凸优化的近端增广拉格朗日（近端AL）框架的复杂性与非线性等式约束。当子问题得到一个近似的一阶（二阶）最优点时，当邻近项系数和罚参数分别满足和时，在外部迭代（其中对于一阶结果和对于二阶结果是用户定义的参数）中可以保证原问题的一阶（二阶）最优点。我们还研究了使用牛顿共轭梯度算法求解子问题时的总迭代复杂度和运算复杂度。最后，我们讨论了一个自适应计划，用于确定一个值的参数，满足分析的要求。
We analyze worst-case complexity of a Proximal augmented Lagrangian (Proximal AL) framework for nonconvex optimization with nonlinear equality constraints. When an approximate first-order (second-order) optimal point is obtained in the subproblem, anfirst-order (second-order) optimal point for the original problem can be guaranteed withinouter iterations (whereis a user-defined parameter withfor the first-order result andfor the second-order result) when the proximal term coefficientand penalty parametersatisfyand, respectively. We also investigate the total iteration complexity and operation complexity when a Newton-conjugate-gradient algorithm is used to solve the subproblems. Finally, we discuss an adaptive scheme for determining a value of the parameterthat satisfies the requirements of the analysis.