If there are two sets of linear constraints in different variables, Ax <= b with x_l <= x <= x_u and Cy <= d with y_l <= y <= y_u, and a set of equality constraints of a specific nonlinear but convex form relating the two sets of variables e^y  x = 0, is the feasible space convex, and what is the proof behind the answer? The difficulty seems to me that the equality constraint would be equivalently formulated as e^y  x <= 0 and e^y  x >= 0, which means that one of these inequalities would be convex and the other would be concave, which may somehow create concavities in the feasible space.
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