On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints
研究在球交集与线性不等式约束下最小化不定二次函数的问题，通过转化为扩展信任域子问题并利用交替方向乘子法和分支定界算法求解，数值实验表明方法有效。
Abstract In this paper, we study the minimization of an indefinite quadratic function over the intersection of balls and linear inequality constraints (QOBL). Using the hyperplanes induced by the intersection of each pair of balls, we show that the optimal solution of QOBL can be found by solving several extended trust-region subproblems (e-TRS). To solve e-TRS, we use the alternating direction method of multipliers approach and a branch and bound algorithm. Numerical experiments show the efficiency of the proposed approach compared to the CVX and the extended adaptive ellipsoid-based algorithm.