# hw6 - Math 171A: Linear Programming Instructor: Philip E....

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Math 171A: Linear Programming Instructor: Philip E. Gill Winter Quarter 2011 Homework Assignment #6 Due Friday February 18, 2011 Starred exercises require the use of Matlab . Exercise 6.1. * (a) Consider the matrix of active constraints A a = - 1 - 8 4 - 7 - 3 - 4 2 0 4 - 2 - 6 0 - 3 3 5 0 0 5 2 7 . Use solve.m to construct a direction p along which the residual of the third constraint increases, but all the other residuals remain the same. If the rows of A a are labeled 1 through 4, what are the indices of the active set after a positive step along this direction? (b) Repeat part (a) for the vertex A a = 0 3 6 - 5 - 4 9 1 6 - 4 5 0 1 6 - 5 - 4 - 3 - 4 - 5 3 2 3 5 - 6 3 2 - 8 - 3 0 7 - 1 - 1 0 0 0 0 . Comment on your results. Is the vertex degenerate or nondegenerate? Exercise 6.2. Let A a be a nonzero m × n matrix, and let C N denote the normal cone C N = { w : w = A T a λ, λ 0 } . (a)

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## hw6 - Math 171A: Linear Programming Instructor: Philip E....

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