mathematical optimization - multiplication of decision variables -


i have programming formulation paper , want give tool solving specific problems. authors stated linear programming (lp) instance, not sure. formulation follows:

max x1+x2+x3...  s.t.  x1.x3+x4.x5 <= 10  x2.x5+x3.x7+x1.x9 <=10  ...

i tried program through cplexqcp function (due quadratic constraints, constraints not include x_i^2 variable). receive cplex error 5002: q in %s not positive semi-definite error. instance of non-linear programming non-convex constraints? can solve cplex or use nlp tool it? newbie lp/nlp staff (do not take course regarding them), welcome explaining details of answers of questions.

thanks much.

the problem posted needs information on domain of variables x1, x2 , x3.

if continuous, there no way express problem linear program (lp), since surface of x1*x2 non-linear.

if @ least 1 of product variables binary (integer), product can linearized (so if have mixed integer program) described in here - since "borders" of above product linear.

cplex can solve classes of quadratic problems. judging error message, problem not belong in there. solving problem, need stick general purpose nlp solver. sample list of solvers can found here, of can triggered software ampl, or can used standalone. no expert here, can not give advice solver should preferred problem.

regards, martin


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