  We investigate numerically the effect of the competition of disorder,
nonlinearity, and boundaries on the Anderson localization of light waves in
finite-size, one-dimensional waveguide arrays. Using the discrete Anderson -
nonlinear Schr\"odinger equation, the propagation of the mode amplitudes up to
some finite distance is monitored. The analysis is based on the calculated
localization length and the participation number, two standard measures for the
statistical description of Anderson localization. For relatively weak disorder
and nonlinearity, a higher disorder strength is required to achieve the same
degree of localization at the edge than in the interior of the array, in
agreement with recent experimental observations in the linear regime. However,
for relatively strong disorder and/or nonlinearity, this behavior is reversed
and it is now easier to localize an excitation at the edge than in the
interior.
