The paper discusses a widely spread range of linear multivariable systems whose most important property is that the self-effect in each control loop or channel is positive while cross-effects are negative. Most of the various tools can be used in their mathematical description such as sets of linear algebraical or integral equations, and elliptical or parabolic partial equations. Optimization problems for this class of systems, referred to as S-problems, feature a number of properties not inherent in linear optimization problems of general form. Thus solution of the dual S-problem which determines the qualitative solution (solution structure) of the direct problem is independent of its functional. The computing procedure applicable to all types of S-problems features monotonic convergence of successive variable approximations to their optimal values.