We consider the Bipartite Boolean Quadratic Programming Problem (BQP01), which generalizes the well-known Boolean quadratic programming problem (QP01). The model has applications in graph theory, matrix factorization and bioinformatics, among others. The primary focus of this paper is on studying the structure of the Bipartite Boolean Quadric Polytope (BQP${}^{m,n}$) resulting from a linearization of a quadratic integer programming formulation of BQP01.

We present some basic properties and partial relaxations of BQP${}^{m,n}$, as well as some families of facets and valid inequalities. We find facet-defining inequalities including a family of odd-cycle inequalities. We discuss various approaches to obtain a valid inequality and facets from those of the related Boolean quadric polytope. The key strategy is based on rounding coefficients, and it is applied to the families of clique and cut inequalities in BQP${}^{m,n}$.

我们考虑二部布尔二次规划问题(BQP01)，它概括了众所周知的布尔二次规划问题 (QP01)。该模型在图论、矩阵分解和生物信息学等领域都有应用。本文的主要重点是研究二部布尔二次多胞体(BQP) 的结构${}^{米,n}$) 由 BQP01 的二次整数规划公式的线性化产生。

我们介绍了 BQP 的一些基本属性和部分松弛${}^{米,n}$，以及一些方面和有效不等式的家庭。我们发现了定义方面的不等式，包括一系列奇数周期不等式。我们讨论了从相关布尔二次多面体的不等式和方面获得有效不等式和方面的各种方法。关键策略基于舍入系数，应用于BQP中的clique和cut不等式的族${}^{米,n}$.