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 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. The validity of a method based (10[1])on these quantities follows because the contours of two functions must be tangent, so their normal vectors must be parallel. The gradient (-5[1])of the objective is set equal to one of these quantities times another gradient in a method of constrained optimization. For 10 points, lambda (10[1])denotes what “multipliers” named (10[1])for a French mathematician? ■END■