On Equivalence of Linear Problems of Efficiency and Risk Control under Uncertainty

Linear two-criteria problems of efficiency and risk control are considered. The minimax risk function and the risk function in the polyhedral 1-metric as risk assessment are used. Two-criteria problems are formalized in the form of the sum type convolution of the efficiency and risk criteria and of the ratio type convolution. It is shown that the solutions of the corresponding linear decision-making problems coincide. The relations are found in the explicit form between the parameters of all problems for which they are equivalent.