AbstractIn this paper the problem of unistage selection with inequality constraints is formulated. If the predictor and criterion variables are all normally distributed, this problem can be written as a convex programming problem, with a linear objective function and with linear constraints and a quadratic constraint. Using the duality theory, for convex nonlinear programming it is proved, that its dual problem can be transformed into a convex minimization problem with non‐negativity conditions. Good computational methods are known for solving this problem. By the help of the dual problem sufficient conditions for a solution of the original primal problem are derived and illustrated by an example of practical interes