In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove that this minimization problem is in the complexity class $P$. The implementation aspects are also described in detail with a special emphasis on the transformation of the quadratic program into a linear program that can be solved in polynomial time. The algorithm was implemented in MATLAB and checked by generating five million matrices of arbitrary dimensions up to 30 with random entries in the range $\left[ -50,50\right] $. All the experiments carried out have revealed that the method works correctly.
翻译：在本文中,在多元时间里开发了一种精确的算法来解决不受限制的二进制二次方程式。 计算的复杂性是 $O\left (n ⁇ frac{15 ⁇ 2 ⁇ right) $, 虽然非常保守, 足以证明这个最小化的问题是在复杂的等级$P$。 执行方面也有详细描述, 特别侧重于将四进制程序转换成一个在多元时间里可以解决的线性程序。 该算法在 MATLAB 中实施, 并通过生成500万个任意尺寸的矩阵, 最多30个, 随机输入范围$\left[ 50, 50\right] $。 所有实验都显示该方法运作正确 。
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