Table 7.4 shows several constraint matrices A (or At) of standard-form LPs and the corresponding projection matrices
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Table 7.4 shows several constraint matrices A (or At) of standard-form LPs and the corresponding projection matrices P (or Pt). Use these results to compute the feasible direction for the specifed equality constraints that is nearest to the given direction
d, and verify that the result satisfies feasible direction conditions at any interior point solution.
(a) x1 + 2x2 + x3 = 4 and d = 13, -6, 32
- 2x1 + x2 = -1
(b) 3x1 + x2 + 4x3 = 4 and d = 12, 1, -72 x2 - 2x3 = 1
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