MATH 305 Lecture Notes - Lecture 12: Elementary Matrix, California State Route 1, Simplex Algorithm
19 May 2016
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Theorem 4. 4. 1 let t1 be the initial tableau for an lp problem in canonical form. Tr+1 be the sequence of tableaus resulting from r pivots by the simplex method; let p1, p2, , pr be the pivoting matrixes that produce these tableaus; and let d = pr pr-1 p2 p1. Then (i) t r +1 = d t1 (ii) d can be partitioned as d = Where r is an m m matrix, s is an 1 m matrix, 0 is an m 1 matrix. Example 1: consider this lp problem (a) pivot the initial tableau twice to get to t3. To proof 4. 4. 2 using book"s proof (method 1), we need the theorem 4. 2. 5. Lemma (theorem 4. 2. 5): suppose that t* is derived from t through a sequence of pivot operations, and let d be the pivoting matrix such that t* = dt.
