An efficient PGM-based algorithm with backtracking strategy for solving quadratic optimization problems with spherical constraint

Abstract

We utilize projected gradient method (PGM for short) to solve quadratic optimization problem with spherical constraint. Based on the global convergence of simple first order conic method for trust region subproblem, we show that under some conditions, the global convergence of the PGM is guaranteed if the initial point is chosen specially. With only the multiplication of matrix and vector involved, a good approximation solution can be obtained in a low computation cost for large scale applications.