We propose a convex quadratic programming (CQP) relaxation for multi-ball constrained quadratic optimization (MB). (CQP) is shown to be equivalent to semidefinite programming relaxation in the hard case. Based on (CQP), we propose an algorithm for solving (MB), which returns a solution of (MB) with an approximation bound independent of the number of constraints. The approximation algorithm is further extended to solve nonconvex quadratic optimization with more general constraints. As an application, we propose a standard quadratic programming relaxation for finding Chebyshev center of a general convex set with a guaranteed approximation bound.

中文翻译：

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多球约束二次优化和扩展的价格便宜的松弛和更好的逼近

我们为多球约束二次优化（MB）提出了凸二次规划（CQP）松弛。（CQP）在困难情况下等效于半定编程松弛。基于（CQP），我们提出了一种求解（MB）的算法，该算法返回的（MB）的解的近似范围与约束数量无关。近似算法被进一步扩展以解决具有更一般约束的非凸二次优化。作为一种应用，我们提出了一种标准的二次规划松弛方法，用于寻找具有保证的近似边界的一般凸集的Chebyshev中心。