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Questions tagged [primal]

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Graphical understanding of the primal and dual problem

I have a relatively simple question. Assuming we have a simple numerical example of an LP with two decision variables and two constraints (non-negativity excluded), how can I visualize the graphical ...
Derd Cff's user avatar
2 votes
1 answer
205 views

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

I am looking for a practical method to find a valid upper bound for the infinity norm of the solution to a standard linear optimization problem: \begin{align}\min&\quad c^\top x \\ \text{s.t.}&...
Ramin Fakhimi's user avatar
2 votes
1 answer
347 views

Finding the dual problem of a minimum problem

How to convert the following primal problem into its dual problem: \begin{align} \min_{x,z}&\quad a^\top x + b^\top z\\\text{s.t.}&\quad Ax-d \le Cz \\&\quad x\ge 0, z \le 0. \end{align} I ...
bm1125's user avatar
  • 131
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1 answer
2k views

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

If optimal solution to the primal is degenerate, does it necessarily follow that optimal solution to dual not unique? That is, is uniqueness an unnecessary assumption? Spin-off from here. In my ...
BCLC's user avatar
  • 59
2 votes
1 answer
149 views

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

I need to solve an LP-relaxation of an airline crew pairing optimization problem (CPOP). The problem formulation is a modified SCP and is as follows: Primal of the CPOP: \begin{align}\min&\quad\...
Divyam Aggarwal's user avatar