This paper describes a method of minimizing a strictly convex quadratic functional of several variables constrained by a system of linear inequalities. The method takes advantage of strict convexity by first computing the absolute minimum of the functional. In the event that the values of the variables yielding the absolute minimum do not satisfy the constraints, an equivalent and simplified quadratic problem in the “Lagrange multipliers” is derived. An efficient algorithm is devised for the transformed problem, which leads to the solution in a finite number of applications. A numerical example illustrates the method.