Hi, all,

I write a simple QCP problem as follows, and I used different solvers to solve it. But, some of them, such as CONOPT, IPOPT, cannot get the optimal solution.

Clearly, the optimal solution is x=1, the optimal objective value is -1. However, some solvers return x=0.

Could someone help me solve this problem?

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positive variable x;

free variable y;

Option optca=0;

Option optcr=0;

x.up=1.0;

equation

obj,

cons1;

obj .. y=e=-x;

cons1 .. x*(x-1)=g=0;

model problem /obj,cons1/;

solve problem using qcp minimzing y;

display x.l,y.l;

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## Cannot get optimal solution for a very simple model

### Re: Cannot get optimal solution for a very simple model

That is not surprising. Conopt, Ipopt, Snopt, ... are

-Michael

*local*solvers. They terminate in a local optimum (KKT conditions are fulfilled). You see this in the model status:***** MODEL STATUS 2*. You need a solver with a global perspective to get the global optimum for a non-convex problem as yours, e.g. Antigone, Baron, ... (see solver table at https://www.gams.com/latest/docs/S_MAIN ... ODEL_TYPES and check the last column 'Global'). You can also pay more attention to your**Locally**Optimal*starting point*. The Conopt manual (https://www.gams.com/latest/docs/S_CONO ... IAL_VALUES) is a good source for information on that.-Michael