We consider the problem [GRAPHICS] where f(l), ..., f(m):R-n --> R-n are (generally nonlinear) differentiable functions, Omega subset of R-n and n, m can be large. We Introduce a new algorithm for solving this problem that can be implemented in rather modest computer environments. The new method is based on a fast one-dimensional newtonian procedure applied to the objective value of an auxiliary function. We report numerical experiments, which suggest that the new algorithm, combined with a powerful strategy for minimization on spheres, can be an effective tool for solving initial vector coding problems.6441732273284