Globally maximizing the sum of squares of quadratic forms over the unit sphere

  • Xiaoli Cen
  • Yong XiaEmail author
Original Paper


We first lift the problem of maximizing the sum of squares of quadratic forms over the unit sphere to an equivalent nonlinear optimization problem, which provides a new standard quadratic programming relaxation. Then we employ a simplicial branch and bound algorithm to globally solve the lifted problem and show that the time-complexity is linear with respect to the number of all nonzero entries of the input matrices under certain conditions. Numerical results demonstrate the efficiency of the new algorithm.


Polynomial optimization Sum of squares Quadratic programming Branch-and-bound 



This research was supported by National Natural Science Foundation of China under Grants 11822103, 11571029, 11771056 and Beijing Natural Science Foundation Z180005.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LMIB of the Ministry of Education, School of Mathematical SciencesBeihang UniversityBeijingPeople’s Republic of China

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