In 2013, Buchheim and Wiegele introduced a quadratic optimisation problem, in which the domain of each variable is a closed subset of the reals. This problem includes several other important problems as special cases. We study some convex sets and polyhedra associated with the problem, and derive several families of strong valid inequalities. We also present some encouraging computational results, obtained by applying our inequalities to (a) integer quadratic programs with box constraints and (b) portfolio optimisation problems with semi-continuous variables.

中文翻译：

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具有域约束的二次优化的有效不等式

2013 年，Buchheim 和 Wiegele 引入了二次优化问题，其中每个变量的域都是实数的封闭子集。这个问题包括其他几个作为特殊情况的重要问题。我们研究了一些与问题相关的凸集和多面体，并推导出了几个强有效不等式。我们还提出了一些令人鼓舞的计算结果，这些结果是通过将我们的不等式应用于（a）具有框约束的整数二次程序和（b）具有半连续变量的投资组合优化问题而获得的。