On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints

Abstract

In this paper, we study the minimization of an indefinite quadratic function over theintersection of balls and linear inequality constraints (QOBL). Using the hyperplanesinduced by the intersection of each pair of balls, we show that the optimal solution ofQOBL 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 anda branch and bound algorithm. Numerical experiments show the efficiency of theproposed approach compared to the CVX and the extended adaptive ellipsoid-basedalgorithm