论文标题
对任意订单不受约束的非convex优化的不精确信任区域算法的强烈评估复杂性
Strong Evaluation Complexity of An Inexact Trust-Region Algorithm for Arbitrary-Order Unconstrained Nonconvex Optimization
论文作者
论文摘要
介绍了使用不精确函数和衍生词值的信任区域算法，以解决无约束的平滑优化问题。该算法使用高阶泰勒模型，并允许搜索强烈的任意顺序最小化。在标准条件下，查找使用该算法的$ q $最小化的评估复杂性将显示为$ \ Mathcal {o} \ big（\ min_ {\ min_ {j \ in \ {1，\ ldots，q \}，q \}}}}}^^^^^^^y（q+1）$阈值。值得注意的是，该顺序与使用精确信息的经典信任区域方法相同。
A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems. This algorithm uses high-order Taylor models and allows the search of strong approximate minimizers of arbitrary order. The evaluation complexity of finding a $q$-th approximate minimizer using this algorithm is then shown, under standard conditions, to be $\mathcal{O}\big(\min_{j\in\{1,\ldots,q\}}ε_j^{-(q+1)}\big)$ where the $ε_j$ are the order-dependent requested accuracy thresholds. Remarkably, this order is identical to that of classical trust-region methods using exact information.
