A Substitute Inverse for the Basis of a Staircase Structure Linear Program
Richard D. Wollmer · Mathematics of Operations Research · 1977
The constraints of a staircase structure linear program are of the following form: A 1 x 1 = d 1 ; B t−1 + A t x t = d t (t = 2, …, T). Letting m i be the number of constraints m period i the substitute inverse consists of the inverse of T matrices which are m i × m i = 1, …, T, as opposed to the actual inverse which is m × m, m = ∑m i . Updating the substitute inverse consists of updating some, but not necessarily all, of the T inverses. This may be done by appending one or more columns and pivoting on them or by adding a dyad matrix. Applications to the PILOT energy model will be discussed.