Hi, I have an optimization problem (primal problem) which is solved by the duality theorem. So I have constraints of the dual and its variable's value. it is worth mentioning the problem is linear. how can I calculate primal variables indirectly and by the dual answer?
The values of the primal are the shadow prices of the constraints of the dual
Use the complementarity slackness conditions, which state that at an optimum solution to an LP each (non-zero) primal variable value times the slack in the corresponding constraint in the dual equals zero. By symmetry, a positive dual variable value implies that the corresponding primal constraint is fulfilled with equality.
I belieive this problem is well described here: https://math.stackexchange.com/questions/288213/how-the-dual-lp-solves-the-primal-lp
Nolberto Munier thank you. in linear programming, it is impossible to calculate Dual and Primal Simultaneously in this way.
Michael Patriksson complementarity slackness condition, while most of the slack variables are not zero, gives a high level of freedom to solve primal. so it does not work.
Kjetil K. Haugen I am reading this title. thank you for introducing.
You can of course also utilise the fact that the primal and dual optimal values are the same - that cuts out one unknown. How many are then left?
Dear Maria
The Solver gives those values simultaneously. After you find the optimal go to 'Reports' and then 'Sensitivity' , and will find there the shadow prices corresponding to binding criteria for the primal solution
Thank you all friends. I added all the primal constraints with the strong duality constraint which connects primal and dual variables together. it worked and primal and dual variables were calculated simultaneously by the solver.
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