论文标题
优化随机高维函数：结构和算法
Optimization of random high-dimensional functions: Structure and algorithms
论文作者
论文摘要
副本对称性打破了假设，即旋转玻璃哈密顿量接近最佳的具有超级结构。也就是说，在Optima附近可以与树的叶子相关联，它们之间的欧几里得距离对应于沿着这棵树的距离。我们调查了在混合$ p $ spin旋转玻璃型号的背景下，对这张照片进行严格证明的最新进展。我们尤其关注以下主题：$（i）$〜哈密顿人关键点的结构； $（ii）$〜实现超级树作为合适的自由能的最佳选择； $（iii）$〜利用此图片的有效优化算法的构建。
Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the Euclidean distance between them corresponds to the distance along this tree. We survey recent progress towards a rigorous proof of this picture in the context of mixed $p$-spin spin glass models. We focus in particular on the following topics: $(i)$~The structure of critical points of the Hamiltonian; $(ii)$~The realization of the ultrametric tree as near optima of a suitable TAP free energy; $(iii)$~The construction of efficient optimization algorithm that exploits this picture.
