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• Gurobi Staff

Did I misunderstand the meaning of Start and VarHintVal? What is the best way to achieve this?

As you mentioned yourself, Start and VarHintVal only guide the solver to the solution. They do not guarantee that the final solution is anywhere near the values provided by Start and VarHintVal.

You could introduce a penalty term to your objective for $$x$$ being far away from $$s$$ and $$y$$ being far away from $$0$$. Or alternatively, if you know that your assumption definitely holds for the optimal solution point, you could introduce bounds  $$s - \delta \leq x \leq s + \delta$$ and $$- \delta \leq y \leq \delta$$ with $$\delta > 0$$.

Best regards,
Jaromił