论文标题
从功能表达式中提取结构，以使MINLP的连续和离散放松
Extracting structure from functional expressions for continuous and discrete relaxations of MINLP
论文作者
论文摘要
在本文中，我们为MINLP中的非线性表达式开发了新的连续和离散的放松。与可分配的编程相反，我们的技术通过使用[12]中首先提出的技术将内部功能结构封装在多面体集合中。我们收紧了[33,13]中得出的放松，并为无法使用先前技术处理的功能获得新的放松。我们开发了新的基于离散化的混合整体编程放松，与文献中的类似放松相比，您会产生更严格的放松。这些放松利用了捕获内部功能结构的简单，将[8]的增量公式推广到多元函数。特别是，当外部功能是超模型时，我们的制剂所需的连续变量比任何先前已知的公式都要少。
In this paper, we develop new continuous and discrete relaxations for nonlinear expressions in an MINLP. In contrast to factorable programming, our techniques utilize the inner-function structure by encapsulating it in a polyhedral set, using a technique first proposed in [12]. We tighten the relaxations derived in [33,13] and obtain new relaxations for functions that could not be treated using prior techniques. We develop new discretization-based mixed-integer programming relaxations that yield tighter relaxations than similar relaxations in the literature. These relaxations utilize the simplotope that captures inner-function structure to generalize the incremental formulation of [8] to multivariate functions. In particular, when the outer-function is supermodular, our formulations require exponentially fewer continuous variables than any previously known formulation.
