In this question, we prove that pivoting over simplex tableau is equivalent to moving from one...
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In this question, we prove that pivoting over simplex tableau is equivalent to moving from one BFS to another BFS. Suppose that a is a BFS for a standard form linear optimization problem min er s. t. Ar=b, r20 where A € Rmxn has full row rank. Consider nonbasic variable , and define a feasible solution y := x+0*d where dB = -B-¹Aj, dj = 1, di = 0 for all nonbasic indices i #j, and 0* is picked from minimum ratio test: XB(1) dB(1) min i=1.....m s.t. dB(0) 50- JB(i) dB(₁), Prove that y is a BFS and that pivoting from a to y one basic variable B(1) leaves basis and one nonbasic variable x, enters the basis. In this question, we prove that pivoting over simplex tableau is equivalent to moving from one BFS to another BFS. Suppose that a is a BFS for a standard form linear optimization problem min er s. t. Ar=b, r20 where A € Rmxn has full row rank. Consider nonbasic variable , and define a feasible solution y := x+0*d where dB = -B-¹Aj, dj = 1, di = 0 for all nonbasic indices i #j, and 0* is picked from minimum ratio test: XB(1) dB(1) min i=1.....m s.t. dB(0) 50- JB(i) dB(₁), Prove that y is a BFS and that pivoting from a to y one basic variable B(1) leaves basis and one nonbasic variable x, enters the basis.
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Proof Let us first prove that y is a BFS Since A has full row rank the columns of A are linearly independent which means that the columns of A indexed ... View the full answer
Related Book For
Computer Networking A Top-Down Approach
ISBN: 978-0136079675
5th edition
Authors: James F. Kurose, Keith W. Ross
Posted Date:
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