论文标题
算法随机二元性理论 - 大型笨拙
Algorithmic random duality theory -- large scale CLuP
论文作者
论文摘要
基于我们的\ bl {\ textbf {随机双重性理论（rdt）}}，按照我们最近的论文的顺序\ cite \ cite {stojnicclupint19，stojnicclupcmpl19，stojnicclupplt19}，我们引入了强大的algorith and text \ textb} cl \ bl.blff。用于解决多项式时间的硬性优化问题，用于求解\ textbf {\ emph {\ emph {}}。在这里，我们进一步移动事物，并利用了我们在一长串工作中建立的另一个出色的RDT功能\ cite {Stojniccsetam09，StojniccsetAmblock09，Stojnicisit2010binary，Stojnicdiscpercp13，Stojnicuperd10，Stojnicupper10，Stojnic Genlasso10，Stojnicgensocp10，Stojnicpsocp10，Stojnicregrnddlt10，Stojnicbinary16fin，Stojnicbinary16asym}。也就是说，除了表征各种随机结构和优化问题的性能时，RDT同时还提供了一种几乎无与伦比的方法来创建实现此类性能的几乎无与伦比的方法。取得成功的关键之一是我们能够将初始\ textbf {\ emph {condrated}}优化转换为\ textbf {\ emph {demph {noctainsed}}}的能力，并且在概念上和计算上都非常简化了事物。最终使我们能够在非常大的规模水平上解决一系列古典优化问题。在这里，我们演示了这种思维如何也可以应用于笨蛋，并最终用于解决\ cite {stojnicclupint19，stojnicclupcmpl19，stojnicclupplt19}的基本问题几乎可以解决的任何问题。
Based on our \bl{\textbf{Random Duality Theory (RDT)}}, in a sequence of our recent papers \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19}, we introduced a powerful algorithmic mechanism (called \bl{\textbf{CLuP}}) that can be utilized to solve \textbf{\emph{exactly}} NP hard optimization problems in polynomial time. Here we move things further and utilize another of remarkable RDT features that we established in a long line of work in \cite{StojnicCSetam09,StojnicCSetamBlock09,StojnicISIT2010binary,StojnicDiscPercp13,StojnicUpper10,StojnicGenLasso10,StojnicGenSocp10,StojnicPrDepSocp10,StojnicRegRndDlt10,Stojnicbinary16fin,Stojnicbinary16asym}. Namely, besides being stunningly precise in characterizing the performance of various random structures and optimization problems, RDT simultaneously also provided an almost unparallel way for creating computationally efficient optimization algorithms that achieve such performance. One of the keys to our success was our ability to transform the initial \textbf{\emph{constrained}} optimization into an \textbf{\emph{unconstrained}} one and in doing so greatly simplify things both conceptually and computationally. That ultimately enabled us to solve a large set of classical optimization problems on a very large scale level. Here, we demonstrate how such a thinking can be applied to CLuP as well and eventually utilized to solve pretty much any problem that the basic CLuP from \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19} can solve.
