Penalizing the solver from finding an optimal solution inside the cone of Second Order Conic constraint

Question

Dears

We know that

X*Y>= D^2+T^2 is a second order conic constraint and it is convex.

However, it is there a way to make the solver understand that it is not optimal to find the optimal solution inside the cone and instead, it should find it on the surface of the cone?

Answer 1

Adding any linear objective to the problem will place the solution at the border of feasibility (assuming you don't use an objective in an unbounded direction)