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