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where {{math|λ}} is a set of Lagrange multipliers which come out of the solution alongside {{math|'''x'''}}.
The easiest means of approaching this system is direct solution (for example, [[LU factorization]]), which for small problems is very practical. For large problems, the system poses some unusual difficulties, most notably that the problem is never positive definite (even if {{mvar|Q}} is), making it potentially very difficult to find a good numeric approach, and there are many approaches to choose from dependent on the problem.<ref>
If the constraints don't couple the variables too tightly, a relatively simple attack is to change the variables so that constraints are unconditionally satisfied. For example, suppose {{math|1='''d''' = 0}} (generalizing to nonzero is straightforward). Looking at the constraint equations:
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