RAH for Farkas
- Univ. of Waterloo (Canada)
Besides being a cheer, and an abbreviation of {open_quotes}Redundency and Helly{close_quotes}, RAH is the following pivot algorithm which, for a system of linear equations (tableau), always stops with an equivalent tableau which either has a non-neg basic solution or else which includes an equation which cannot have a non-neg solution: At any stage of the algorithm, along with specifications of a tableau, there is a sequence [N(O), r(1), N(1), r(2), ..., r(q), N(q)], such that {l_brace}r(1), ..., r(q){r_brace} is a subset of the basic columns, and {l_brace}N(0), N(1), ..., N(q){r_brace} is a partition of all the non-basic columns. To start, the sequence is [N(0)]. Choose any basic variable x(i) such that its basic-solution value is negative and such that i is not an r-term of the sequence; if there is no x(i), stop. (Each r-term of the sequence is {open_quotes}redundant{close_quotes} as long as non-basics in earlier terms of the sequence stay non-basic). Choose a term N(t) of the sequence, such that W is at least of size 1 and at most the size of N(t), where W consists of the columns in N(t), N(t+1), ..., or N(q), which are negative in row i. (If there is no such N(t), stop, because equation i is infeasible). Pivot any member j of W into the basis, and pivot i out of the basis. Get a new sequence by not changing any terms earlier than N(t), by letting N(t) to be W - j, but letting r(t) be j, and letting N(t + 1) = N(q) consist of all nonbasics not in earlier terms. As part of the LP methods, RAH improves an oriented-matroid rule of Bland, Edmonds, and Fukuda.
- OSTI ID:
- 35978
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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