  When searching for global optima of nonconvex unconstrained optimization
problems, it is desirable that every local minimum be a global minimum. This
property of having no spurious local minima is true in various problems of
interest nowadays, including principal component analysis, matrix sensing, and
linear neural networks. However, since these problems are non-coercive, they
may yet have spurious local minima at infinity. The classical tools used to
analyze the optimization landscape, namely the gradient and the Hessian, are
incapable of detecting spurious local minima at infinity. In this paper, we
identify conditions that certify the absence of spurious local minima at
infinity, one of which is having bounded subgradient trajectories. We check
that they hold in several applications of interest.
