Many image reconstruction algorithms have been proposed to cope with optical/IR interferometric data. A first difficulty is to deal with the sparsity of the data and the uneven u-v coverage. This is usually overcome by imposing a priori constraints to the sought image. The reconstruction then amounts to solving an optimization problem where fidelity to the data and to the priors must both be satisfied to a chosen level. Due to the type of interferometric measurements, the image restored by the current algorithms depends on some initial guess and on the optimization strategy. Even though the resulting image is often satisfactory, there are no guarantees that the best image is obtained given the data and the constraints. This is a strong defect which may badly impact the interpretation of interferometric observations by astronomers. In this paper, we consider using stochastic methods such as simulated annealing to solve for the problem of image reconstruction with sparse Fourier amplitudes and unknown Fourier phases. This preliminary study is a first step toward image reconstruction with partial Fourier phase information.