论文标题
非convex优化的同质二阶下降方法
A Homogeneous Second-Order Descent Method for Nonconvex Optimization
论文作者
论文摘要
在本文中，我们使用均质的二次近似近似统一的二阶下降法（HSODM）引入了原始函数。同质化的优点是，在每次迭代时，仅计算出梯度 - 亲戚综合基质的最左侧特征向量。因此，该算法是一种单循环方法，不需要切换到其他复杂算法，并且易于实现。我们表明，HSODM的全局收敛速率为$ O（ε^{ - 3/2}）$，以找到$ε$ - 售价二阶固定点，并且在标准假设下具有本地二次收敛率。数值结果证明了所提出的方法比其他二阶方法的优点。
In this paper, we introduce a Homogeneous Second-Order Descent Method (HSODM) using the homogenized quadratic approximation to the original function. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian integrated matrix is computed at each iteration. Therefore, the algorithm is a single-loop method that does not need to switch to other sophisticated algorithms and is easy to implement. We show that HSODM has a global convergence rate of $O(ε^{-3/2})$ to find an $ε$-approximate second-order stationary point, and has a local quadratic convergence rate under the standard assumptions. The numerical results demonstrate the advantage of the proposed method over other second-order methods.
