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Say I have two optimization problems A and B.

If an optimal solution of A is feasible for b and vice versa:

Q 1) Is every optimal solution for A an optimal solution of B (and vice versa)?

Q 2) If the answer to Q1 is false, then is there at least one optimal solution of A that is also an optimal solution of B (and vice-versa)?

rahs
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1 Answers1

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No to both questions, consider these problems:

A: $\min_x \{ x : 0 \leq x \leq 1\}$

B: $\min_x \{ -x : 0 \leq x \leq 1\}$

LinAlg
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