We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a way that both the objective and the constraints are separable convex quadratics. We describe a family of polynomial-time approximation algorithms and negative complexity results.

翻译：我们研究一类凸优化问题，其中互不相交的变量块受二元指示变量控制，且这些指示变量本身也受到约束（例如基数约束）。若干重要问题类别均可表述为此类形式，使得目标函数与约束条件均为可分离的凸二次函数。本文描述了一族多项式时间近似算法，并给出了负面的复杂度结果。