Dear support team,

I have tried to solve an optimization problem (an MINLP) to minimize the number of items that need to be stored. The objective function is as follows:

```
objective function: Minimize z = sum(i, R(i)/x(i))
```

Where, R(i), i in {1, …, n}, given constant and x(i) are integer variables. I have used three different formulations to compare which one may solve the problem faster. First, the above formulation was solved by an MINLP solver. Second, defining the new auxiliary variables and substituting diviation. Third, reformulating the objective function into the rotated second-order cone constraints. What I am interested in is:

In the first case, some of the solvers like Baron or Lindo could solve the problem faster than the second on. In the second case, a solver like SCIP could deal with the problem faster than the first one!. (substituting diviation with product). In the third case, the RSOC model was solved by CPLEX or Xpress efficiently.

It should be noted that In all of the cases the model solved optimality and the results are the same. When I tried to solve the RSOC model by Mosek, as it has some features to encounter with that efficiently, it returned:

The quadratic constraint matrix is not NSD That I think, it is related to the RSOC constraints.

I try using https://www.gams.com/34/docs/UG_LanguageFeatures.html#UG_LanguageFeatures_ConicProgramming_Example to reformulate the problem (as Fred mentioned in my previous email). I this case, the problem contains the integer variables but in the introduction, it has been declared the variables positive or free. Please, see the attached file.

I was wondering if, how we can deal with the integer variables in RSOC?

Best Regards

Abbas

RSOC_Reformulation.gms (957 Bytes)