Nested scalar convolutions in multi-criteria problems

A problem of structuring of the criteria set is considered in case of large dimension multi-criteria problems solving. A notion of the nested scalar convolution is introduced. The optimization problem is to determine the arguments by extremizing the objective function Essentially, this function is a scalar convolution of the criteria vector reflecting the utility function of the decision maker when solving a specific optimization problem. Scalar convolution is the act of composing criteria. A criterion is a measure of the quality of functioning of object in relation to the achievement of the k-th goal. If «more» means «better», then to improve quality this criterion must be maximized. Otherwise, the criterion is minimized. For definiteness, we consider the optimization problem with minimized quality criteria.