论文标题
基于经典的拉格朗日函数
Iteration-complexity of an inner accelerated inexact proximal augmented Lagrangian method based on the classical Lagrangian function
论文作者
论文摘要
本文建立了内部加速不精确的增强拉格朗日（Iaipal）方法的迭代复杂性，用于求解基于经典增强Lagrangian（Al）功能的线性构成的平滑非凸复合优化问题。更具体地说，每种iaipal迭代都包括通过加速复合梯度（ACG）方法不截然不见地求解近端Al子问题，然后再进行经典的Lagrange乘数更新。 Under the assumption that the domain of the composite function is bounded and the problem has a Slater point, it is shown that IAIPAL generates an approximate stationary solution in ${\cal O}(\varepsilon^{-5/2}\log^2 \varepsilon^{-1})$ ACG iterations where $\varepsilon>0$ is a tolerance for both stationarity and可行性。此外，上述结合是在不假定初始点可行的情况下得出的。最后，提出了数值结果，以证明iaipal的强大实践表现。
This paper establishes the iteration-complexity of an inner accelerated inexact proximal augmented Lagrangian (IAIPAL) method for solving linearly-constrained smooth nonconvex composite optimization problems that is based on the classical augmented Lagrangian (AL) function. More specifically, each IAIPAL iteration consists of inexactly solving a proximal AL subproblem by an accelerated composite gradient (ACG) method followed by a classical Lagrange multiplier update. Under the assumption that the domain of the composite function is bounded and the problem has a Slater point, it is shown that IAIPAL generates an approximate stationary solution in ${\cal O}(\varepsilon^{-5/2}\log^2 \varepsilon^{-1})$ ACG iterations where $\varepsilon>0$ is a tolerance for both stationarity and feasibility. Moreover, the above bound is derived without assuming that the initial point is feasible. Finally, numerical results are presented to demonstrate the strong practical performance of IAIPAL.
