If the primal problem has multiple optimal solutions the, Mathematics

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If the primal problem has multiple optimal solutions the

For Optimization problems,

if the primal problem has multiple optimal solutions (the line segment from (x,y) to (x',y')), then does this necessarily imply that the dual problem also has multiple optimal solutions as well, or is it possible that the optimal solution to the dual problem is still unique?

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Mathematics: If the primal problem has multiple optimal solutions the

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