An accelerated procedure for solving binary optimization problems

The problem of minimization of multiextremal quadratic functional constructed in the state space with binary variables is studied. To accelerate the local field (an analog of the gradient in a continuous space), it is proposed to binarize the matrix based on which the functional is constructed, coarsening its entries in sign to the values 0, ± 1. It is shown that the binarization procedure can be performed in an optimal way such that the calculates direction of the local field coincides with considerable probability with its true direction. The procedure is oriented to solving problems in the configuration space of high dimension, since the binarization of the matrix considerably reduces the required amount of main memory and the computational complexity of the algorithm.