Optimization problems with points of discontinuity and discrete arguments.

Minimization of such functions is considered, where some arguments are related to the final function by intermediate functions with discontinuity points, but other arguments have only 0 and 1 for the allowed values, although the theoretical generalization allows also intermediate values. Both of the circumstances create difficulties in the use of the gradient method. We solve the first problem by approximation, primarily by a square polynomial obtained using the integral form of the least squares method, and later by the partial sums of orthogonal series of the wave function treated with the logarithmic averages method. The second problem can be solved with the help of the planes, which have been taken in the n-dimensional space in such a way that any allowed point on the side of the space relative to this plane is better than all the points on the other side. [ABSTRACT FROM AUTHOR]