product of variables in objective function - MathOverflow

product of variables in objective function

2012-09-17T02:39:47Z

Hi there,

I'm looking for a solver that allows me to solve an optimization problem of the form min x1*x2*x3,...,xn subject to some linear constraints. I've used gurobi before, however I couldn't find the way to include products in the objective function as well as in constraints.

Cheers

Guillermo

Answer by Dima Pasechnik for product of variables in objective function

2012-09-17T05:34:00Z

This is a hard problem (maximizing the product is a bit better one, as sometimes one can take $\log$ of the objective function, and it becomes concave...). Your best shot might be to use the sum of squares approach for polynomial optimization, as implemented e.g. in YALMIP.

Answer by joro for product of variables in objective function

2012-09-17T06:20:53Z

Recently discovered minizinc

MiniZinc is a medium-level constraint modelling language. It is high-level enough to express most constraint problems easily, but low-level enough that it can be mapped onto existing solvers easily and consistently. It is a subset of the higher-level language Zinc. We hope it will be adopted as a standard by the Constraint Programming community. FlatZinc is a low-level solver input language that is the target language for MiniZinc. It is designed to be easy to translate into the form required by a solver.

There are several backends for the translated problem (MIP, SAT, etc).

Here is how something similar to your question will look like in minizinc:

var int: a;
var int: b;
constraint a + b <= 10;
constraint a>0;
constraint b>0;
solve maximize a*b;
output [ show([a,b]) ];
=======
[5, 5]