  The Lagrangian of a hypergraph is a crucial tool for studying hypergraph
extremal problems. Though Lagrangians of some special structure hypergraphs
have closed-form solutions, it is a challenging problem to compute the
Lagrangian of a general large scale hypergraph. In this paper, we exploit a
fast computational scheme involving the adjacency tensor of a hypergraph.
Furthermore, we propose to utilize the gradient projection method on a simplex
from nonlinear optimization for solving the Lagrangian of a large scale
hypergraph iteratively. Using the Lojasiewicz gradient inequality, we analyze
the global and local convergence of the gradient projection method. Numerical
experiments illustrate that the proposed numerical method could compute
Lagrangians of large scale hypergraphs efficiently.
