标题： 最优Bregman量化：重新审视最优量化器的存在性和唯一性 显示英文标题

标题： Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited

摘要： 本文重新探讨了关于Bregman散度的 $L^r$ -最优量化存在定理，即 $r\ge 2$，我们建立了生成散度的严格凸函数在较轻的假设下最优量化器的存在性，特别是在二次情形（\($r=2$\））下。 然后我们证明了一个类似于Trushkin的一维唯一性定理，适用于强单峰分布和由严格凸函数生成的散度，这些函数的三阶导数要么是严格 $\log$ -凸的，要么是 $\log$ -凹的。 显示英文摘要

摘要： In this paper we revisit the exsistence theorem for $L^r$-optimal quantization, $r\ge 2$, with respect to a Bregman divergence: we establish the existence of optimal quantizaers under lighter assumptions onthe strictly convex function which generates the divergence, espcially in the quadratic case ($r=2$). We then prove a uniqueness theorem ``\`a la Trushkin'' in one dimension for strongly unimodal distributions and divergences gerated by strictly convex functions whiose thire dervative is either stictly $\log$-convex or $\log$-concave.