[AMPL 1834] Constraint _scon[1] is not convex quadratic since it is equality constraint

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[AMPL 1834] Constraint _scon[1] is not convex quadratic since it is equality constraint

by Chris-616 :: Rate this Message:

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Hello, I got an error message as in the subject while i tried to use
AMPL + Cplex to solve some optimization with the constraint of the
following kind

set D :=1..10;

var x {D};

subject to con1: (min {i in D} x[i]) = ...;

does anybody know the reason for this? thanks a lot!

best,

chris


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[AMPL 1835] Re: Constraint _scon[1] is not convex quadratic since it is equality constraint

by Robert Fourer-2 :: Rate this Message:

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Chris,

CPLEX cannot handle constraints with terms like "min {i in D} x[i]" in them --
specifically, terms using the "min" operator.  This operator makes the
constraint nonlinear, but CPLEX can handle only linear constraints and certain
varieties of convex quadratic constraints.  All of the latter are inequalities;
hence the error message.  ("_scon[1]" refers to the first constraint sent to
the solver.)

Your best hope of using CPLEX to solve problems containing the "min" operator
is probably to convert them to problems in linear constraints.  Depending on
the specifics of the constraints, you might need to introduce some zero-one
integer variables as well.

Bob Fourer
4er@...


> -----Original Message-----
> From: ampl@... [mailto:ampl@...] On Behalf Of Chris
> Sent: Monday, June 16, 2008 2:16 PM
> To: AMPL Modeling Language
> Subject: [AMPL 1834] Constraint _scon[1] is not convex quadratic since it is
> equality constraint
>
>
> Hello, I got an error message as in the subject while i tried to use
> AMPL + Cplex to solve some optimization with the constraint of the
> following kind
>
> set D :=1..10;
>
> var x {D};
>
> subject to con1: (min {i in D} x[i]) = ...;
>
> does anybody know the reason for this? thanks a lot!
>
> best,
>
> chris
>



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[AMPL 1836] Re: Constraint _scon[1] is not convex quadratic since it is equality constraint

by medvall :: Rate this Message:

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With D binary variables you could probably do this transformation (or
similar, not 100 % sure), where prod is the b[i]*x[i], cont is x[i]
and bin is b[i]. Then you can force sum(b[i]) to be 1 and the prod to
be less than or equal to all x[i]. Might be a better way though.

prod <= cont
prod >= cont - x_U * (1 - bin)
prod <= x_U * bin
prod >= x_L * bin

Best wishes, Marcus
Tomlab Optimization Inc.
http://tomopt.com/ampl/
http://tomdyn.com/
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