In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with continuation procedure, boundary value problem associated Based viewpoint Wasserstein Hamiltonian flow initial and target densities, our reflects structure underlying exploits it discretization. Several examples are presented ...

A numerical method is established to solve the problem of minimizing a nonquasiconvex potential energy. Convergence of the method is proved both in the case on its own and in the case when it is combined with a weak boundary condition. Numerical examples are given to show that the method, especially when applied together with a continuation method and some other numerical techniques, is not onl...

The solution methods based on semidefinite programming (SDP) relaxations for sensor network localization (SNL) problems can not handle very large-sized SNL problems. We present a continuation method using the gradient descent method to efficiently solve large-sized SNL problems. We first formulate the problem as an unconstrained optimization problem and then apply the continuation on the distan...