Solving Ill-Posed Problems by Methods of Multicriterion Mathematical Programming

Solving ill-posed problems on the basis of methods of multicriterion mathematical programming is discussed. In method of regularization, by which ill-posed problems are solved, a parameter of regularization is additionally defined, for estimation of which, at present, there are no unambiguously formalized procedures. Methods of mathematical programming allow avoiding this problem and taking into account additional conditions of the problem. As an example, a problem is considered of direction finding of point radio sources with the help of the antenna system consisting of weakly directed elements (vibrators). Algorithms are given of point estimations of amplitudes of signals of bearings and elevations of radio sources; interval estimations are obtained by a method of statistical tests and analytically.