So, let’s say that one is interested in detecting feasibility in a Mixed 0-1 SOCP problem and utilizes the MOSEK solver. Is there a way to force the solver to search for feasibility instead of leaving it try to find the optimal solution? The motivation for such an action is to save some time (if possible) if one doesn’t care for the quality of the solution but to just see if there is one.

Actually sometimes it may find a feasible solution faster if the objective is nonzero. For instance a suitable chosen objective may make the initial continous relaxation having a (near) integer feasible solution.

How to construct such a suitable objective is impossible to say anything about in general.