  Recent theoretical developments in astronomical aperture synthesis have
revealed the existence of integer-ambiguity problems. Those problems, which
appear in the self-calibration procedures of radio imaging, have been shown to
be similar to the nearest-lattice point (NLP) problems encountered in
high-precision geodetic positioning, and in global navigation satellite
systems. In this paper, we analyse the theoretical aspects of the matter and
propose new methods for solving those NLP problems. The related optimization
aspects concern both the preconditioning stage, and the discrete-search stage
in which the integer ambiguities are finally fixed. Our algorithms, which are
described in an explicit manner, can easily be implemented. They lead to
substantial gains in the processing time of both stages. Their efficiency was
shown via intensive numerical tests.
