These quantities are updated at each step by adding a term proportional to a norm penalty rho in an “alternating direction” method developed by Stephen Boyd et al. A function g of these quantities is maximized at a point d* (“d star”), which equals p* (“p star”) only when a “gap” is zero. Both x and one of (15[1])these quantities are held fixed when differentiating in the statement of the envelope theorem. The kth of these quantities times a function gk (“g-sub-k”) is zero for all k under complementary slackness, which is one of the (*) KKT conditions. (10[1])The validity of a method based (10[1])on these quantities (-5[1])follows because the contours (10[1])of two functions (10[1])must (-5[1])be tangent, (10[1])so their normal (10[1])vectors must be parallel. The gradient (-5[1])of the objective is set (10[1])equal to one of these quantities times (10[1])another gradient (-5[1])in a method (10[1])of constrained optimization. (-5[1])For 10 points, lambda (10[1])denotes what (-5[1])“multipliers” (-5[2])named (10[1])for (10[1])a French mathematician? (10[3])■END■ (10[5])