论文标题
渐近近端方法：针对一类多个最小值问题找到具有线性收敛的全局最小值
Asymptotic proximal point methods: finding the global minima with linear convergence for a class of multiple minima problems
论文作者
论文摘要
我们提出和分析渐近近端点（APP）方法，以找到一类非凸，非平滑纸或什至不连续的多个最小功能的全局最小化器。该方法基于非convex近端点的渐近表示，因此它可以找到全局最小化器而不会被困在鞍点，局部最小值甚至不连续性中。我们的主要结果表明，该方法享受此类功能的全局线性收敛。此外，该方法是无衍生的，其触电成本（即功能评估的数量）也有限，因此它具有复杂性绑定的$ \ MATHCAL {O}（\ log \ log \ frac {1}} $ $，可以找到这个点与全球最小值之间的差距，使得差距与全球最小的差距相比$ by by $ $ $ $ε> 0。数值实验和比较在各个方面从$ 2 $到$ 500 $都证明了该方法的好处。
We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of nonconvex proximal points so that it can find the global minimizer without being trapped in saddle points, local minima, or even discontinuities. Our main result shows that the method enjoys the global linear convergence for such a class of functions. Furthermore, the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is also bounded, so it has a complexity bound $\mathcal{O}(\log\frac{1}ε)$ for finding a point such that the gap between this point and the global minimizer is less than $ε>0$. Numerical experiments and comparisons in various dimensions from $2$ to $500$ demonstrate the benefits of the method.
