论文标题
稀疏凸优化工具包：混合构架框架
Sparse Convex Optimization Toolkit: A Mixed-Integer Framework
论文作者
论文摘要
本文提出了一个开源分布式求解器，用于解决计算网络上稀疏凸优化（SCO）问题。稀疏的凸优化工具包（SCOT）在过去的算法优化方面的算法进步的动机中采用了一种混合企业方法来找到用于SCO问题的精确解决方案。特别是，SCOT汇集了各种技术，以将原始的SCO问题转换为等效的凸混合机非线性编程（MINLP）问题，该问题可以从高性能和并行计算平台中受益。为了解决等效的混合企业问题，我们介绍了在基于LP/NLP的分支机构和结合的基础上构建的分布式混合外近似（DIHOA）算法，并针对这种特定的问题结构量身定制。 DIHOA算法结合了所谓的单树外近似值，自然地整合了分布式凸出非线性子问题的分散算法，并利用增强技术，例如二次切割。最后，我们提出了详细的计算实验，这些实验表明了通过分布式数据集对140个SCO问题的数值基准测试求解器的好处。为了显示SCOT的总体效率，我们还提供了将SCOT与其他最先进的MINLP解决器进行比较的性能概况。
This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse Convex Optimization Toolkit (SCOT) adopts a mixed-integer approach to find exact solutions to SCO problems. In particular, SCOT brings together various techniques to transform the original SCO problem into an equivalent convex Mixed-Integer Nonlinear Programming (MINLP) problem that can benefit from high-performance and parallel computing platforms. To solve the equivalent mixed-integer problem, we present the Distributed Hybrid Outer Approximation (DiHOA) algorithm that builds upon the LP/NLP based branch-and-bound and is tailored for this specific problem structure. The DiHOA algorithm combines the so-called single- and multi-tree outer approximation, naturally integrates a decentralized algorithm for distributed convex nonlinear subproblems, and utilizes enhancement techniques such as quadratic cuts. Finally, we present detailed computational experiments that show the benefit of our solver through numerical benchmarks on 140 SCO problems with distributed datasets. To show the overall efficiency of SCOT we also provide performance profiles comparing SCOT to other state-of-the-art MINLP solvers.
