论文标题
痕迹的最坏情况复杂性具有不精确的子问题解决方案，用于非凸平滑优化
Worst-Case Complexity of TRACE with Inexact Subproblem Solutions for Nonconvex Smooth Optimization
论文作者
论文摘要
提出，分析和测试了用于解决非凸平滑优化问题的算法。该算法是带有收缩和扩展的信任区域算法的扩展（跟踪）[数学。 prog。 162（1）：132，2017]。特别是，该扩展允许算法使用出现的子问题的不精确溶液，这是解决大规模问题的重要特征。允许以$ {\ cal o}（ε^{ - 3/2}）$的最佳迭代复杂性的方式允许不精确度，以保持$ε$ - $ -Appproximate的一阶固定点，而与原始跟踪相比，Hessian-vector产品的最坏情况可以显着提高。数值实验显示了允许不精确的子问题解决方案的好处，并且该算法与最先进的技术进行了比较。
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In particular, the extension allows the algorithm to use inexact solutions of the arising subproblems, which is an important feature for solving large-scale problems. Inexactness is allowed in a manner such that the optimal iteration complexity of ${\cal O}(ε^{-3/2})$ for attaining an $ε$-approximate first-order stationary point is maintained while the worst-case complexity in terms of Hessian-vector products may be significantly improved as compared to the original TRACE. Numerical experiments show the benefits of allowing inexact subproblem solutions and that the algorithm compares favorably to a state-of-the-art technique.
