[Scip] FARKAS COEFFICIENT

[dponce at us.es]

Hello SCIP, 

The previous problem I had has been solved. Finally, I found a mistake
in the code. 

Now, when the instance is not too small, my procedure is not working in
some PRICERFARKAS. I found the function SCIPgetVarFarkasCoef(). Is this
the slack of the associated dual constraint? 

My variables are nonnegatives and usually its Farkas coefficient is
nonpossitive. But sometimes I have found possitive Farkas coefficient.
Is this possible? 

Thanks. 

Diego. 

El 24/10/2014 18:57, dponce at us.es escribió: 

> Dear Gerald, 
> 
> answered to your question, all my constraints are modifiable. 
> 
> I have checked all my constraints are contained in the LP and the problem is infeasible. Let me explain in a different way from my previous e-mail what is happening. 
> 
> In my problem x variables are added from the very begining and y variables are the ones to add. 
> 
> My feasible region is Ay = 1 (u) 
> 
> -By >=-b (v) 
> 
> Cx -Dy = 0 (w) where A,B,C,D>=0 b>0 
> 
> x,y>=0 
> 
> in a minimization problem and I guess SCIP is considering Min 0'x+0'y problem since v Farkas multipliers are possitive. 
> 
> So my Farkas dual is Max u' -v'b +w'0 
> 
> w'C <= 0 (x) 
> 
> s.t. u'A-v'B -w'D <= 0 (y) 
> 
> v>=0 
> 
> For the first time I do not have y variables, so the primal is infeasible and SCIP realizes and set my variable isfarkas to TRUE. However, to solve the problem 
> 
> Max u' -v'b +w'0 
> 
> w'C <= 0 (x) 
> 
> v>=0 
> 
> I expect for instance w=0,v=0 and u_1+u_2+...+u_n=e99. So I'd add any y_i variable with u_i*a_i>0, I'd see what is happening and so on until feasibility. 
> 
> But what really is happening is that the solution of the sual farkas is u_j=1 for some j and v_k=e99 for some k. Hence the objective function is 1-b_k*e99=-e99 which is not logical solution for a maximization problem. Are there any function to get the dual Farkas objective? Just to verify. 
> 
> Finally, when I set x variables to binary, if I start with a feasible solution, every time that I am in Farkas I do not add any new variable and the node is closed. By the moment the solutions that I got are correct-I have solved the problem by another approach-, but I can't assure. I think if I solve the mistake for getting a first feasible solution in the LP, it will be enough to assure well done my MILP procedure. 
> 
> Best. 
> 
> Diego. 
> 
> El 24/10/2014 12:58, Gerald Gamrath escribió: 
> Dear Diego,
> 
> I have implemented a branch-and-price-procedure with a pricer which seems working in the PRICERREDCOST. But in the instances that it need to use PRICERFARKAS I am obtaining some farkas multipliers with strange values, like -e99. Indeed this dual variable should be nonnegative. this sounds strange. Can you please check with SCIPgetLPSolstat() that the LP is really infeasible and with SCIProwIsInLP() that the row corresponding to the constraint for which you get the dual farkas multiplier is contained in the LP (you can get the row of a linear constraint with SCIPgetRowLinear()). Did you mark the constraint to be modifiable?
> 
> Because of this problem, I would like to know if SCIP by itself is able to close an infeasible node since the variables fixed avoid any feasible solution AND HOW. Yes, SCIP can detect the infeasibility of a node in the domain propagation step. For example, if you have a constraint x + y = 1 and x and y were both fixed to 0, SCIP will detect the infeasibility and cut off the node. However, this is only done if the constraint was not marked to be modifiable, since otherwise pricing might add more variables to the constraint and there might still be feasible solutions with x = y = 0.
> 
> My Farkas pricing is similar to the Reduced cost pricing whith 0 in the coefficients of the objective function and SCIPgetDualfarkasLinear() instead of SCIPgetDualsolLinear(). This is how it should be.
> 
> Best,
> Gerald

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