Is this function convex in all cases? I have some doubts


Presuming the denominators are nonnegative, the d terms can be handled with inv_pos,. which automatically imposes nonnegativity constraint on its argument.

There are then product terms between binary and inv_pos Those can be linearized by Big M modeling, presuming you can impose an upper bound on the d terms. I think that can work, even though inv_posis convex and non-affine, because the lower bound inequalities for the lower bound Big M constraints (which would be non-convex) can be omitted due to always being true anyhow. That leaves only the convex Big M constraints. See “Product values” at . in which you would treat inv_pos(...) as the continuous variable. You better check to make sure I don’t make a logic error in making this assessment.