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A class of valid inequalities for multilinear 0-1 optimization problems

机译：多线性0-1优化问题的一类有效的不等式

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This paper investigates the polytope associated with the classical standard linearization technique for the unconstrained optimization of multilinear polynomials in 0-1 variables. A new class of valid inequalities, called 2-links, is introduced to strengthen the LP relaxation of the standard linearization. The addition of the 2-links to the standard linearization inequalities provides a complete description of the convex hull of integer solutions for the case of functions consisting of at most two nonlinear monomials. For the general case, various computational experiments show that the 2-links improve both the standard linearization bound and the computational performance of exact branch & cut methods. The improvements are especially significant for a class of instances inspired from the image restoration problem in computer vision. The magnitude of this effect is rather surprising in that the 2-links are in relatively small number (quadratic in the number of terms of the objective function). (C) 2017 Elsevier B.V. All rights reserved.
机译：本文研究了0-1变量在多线性多项式的无约束优化的经典标准线性化技术相关的多阱。引入了一个新的有效不等式，称为2个环节，以加强标准线性化的LP弛豫。添加到标准线性化不等式的2个链路提供了对由最多两个非线性单体组成的功能的整数解决方案的凸壳的完整描述。对于常规情况，各种计算实验表明，2连通性改善了标准线性化绑定和精确分支和切割方法的计算性能。对于从计算机视觉中的图像恢复问题激发的一类实例来说，改进尤为重要。这种效果的大小相当令人惊讶地认为，2连杆处于相对较小的数量（以目标函数的术语数量二次）。 （c）2017 Elsevier B.v.保留所有权利。

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