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4 votes

Is optimal solution to dual not unique if optimal solution to the primal is degenerate?

If I understand your question correctly, I think you can find your answer by considering the following two primal problems. The first is \begin{alignat*}{2} & \max & x_{1}\\ & \textrm{s....
prubin's user avatar
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3 votes
Accepted

On dual-formulation of a given primal for a set-covering problem

It does not look correct, and in particular the dual of an LP is an LP, so it makes no sense to have a binary variable in the dual. I suspect what led you astray was a misunderstanding of the penalty ...
prubin's user avatar
  • 39.5k
3 votes

An upper bound for the norm of solution to linear optimization problem

Unless I misunderstand your problem you can get a bound on the norm of x by finding upper bounds for each component of x. You can use primal and dual bound tightening to get upper bounds on each x. ...
Philipp Christophel's user avatar
2 votes
Accepted

Finding the dual problem of a minimum problem

Primal Problem $$\begin{align} \text{minimize} \quad & \sum_{i=1}^n a_i x_i + \sum_{i=1}^n b_i z_i \\\ \text{subject to} \quad & A\mathbf x-\mathbf d \le C\mathbf z \\ & x_i \ge 0 \quad \...
marco tognoli's user avatar

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