I have a Mixed Integer Quadratic problem that is coded by GAMS software. (non convex quadratic objective function with linear constraints product of two continuous variables in the objective function makes it non convex) I have confronted with two serious problems after running the model and ask you for help: 1 first,I use to solve my problem using CPLEX solver by setting optimality target as 3, but unfortunately the solution returned by the GAMS is not feasible, however Cplex reports Gap!!!! and it seems that some of constraints are not considered in the presented solution.(it is remarkable that the model had a time limitation.) is it possible that the GAMS software returns an infeasible solution?and what is the reason of this happening? 2secondly, I used to solve the problem using Baron solver. I got "the problem is infeasible" error..but when I deleted the quadratic term of objective function which makes it non convex , Baron could solve the problem without any error!!! does the problem feasiblity change by changing the objective function? would you please explain the reason and the way I can solve it.. asked 31 Jul '16, 04:53 m_bk 
Perhaps you have some horrible scaling on the quadratic term, and that is degrading the numerics of the problem so severely as to make what is actually a feasible problem appear to the solver (possibly after some internal transformations) to be infeasible. answered 31 Jul '16, 11:18 Mark L Stone thanks for your reply. what do you mean by horrible scaling on the quadratic term? the quadratic term obtained by multiplying two continuous (and positive) variables in objective function. your help is really appreciated
(01 Aug '16, 01:46)
m_bk
Can you show your whole model here?
(01 Aug '16, 07:29)
Mark L Stone
Perhaps you are using Big M modeling, and your M is too big, so big that it is causing numerical problems for the solver. You want your big M to be (just) big enough, but not so big that it causes numerical problems.
(02 Aug '16, 07:48)
Mark L Stone
Note that if you use YALMIP, it can do the big M modeling for you, and produce a just big enough M automatically, providing that you bound all the appropriate variables. See http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.BigMAndConvexHulls .
(02 Aug '16, 07:59)
Mark L Stone
I really thanks for your kind help. yes The big M was the main problem
(08 Aug '16, 07:14)
m_bk
