A sum of coefficents multiplying a sequence of terms $\sum_i a_i t_i$ is a linear combination. We get more specific types of combinations when we make further assumptions. In particular, if we assume $0 \leq a_i$ and $\sum a_i = 1$, we obtain a convex combination / a convex set / a simplex.
In my application, I am lead to consider coefficients that also satisfy the non-negativity assumption $0 \leq a_i$, but instead of summing to one, I require summing to one or less, $\sum a_i \leq 1$.
I'm currently running with an explicit statement in my write-up, but it is a bit lengthy.
any linear combination of the components such that the coefficients are non-negative and such that the sum of the coefficient is smaller than or equal to $1$ gives rise to ...
"subconvex" sounds fitting and concise:
any subconvex combination of the components gives rise to ...
But I never heard this expression before, so I'm reluctant to use it. Is there a name for such combinations? If there is no standard terminology for this concept, would there be a more elegant explicit formulation than my current statement? I'm only using this concept once for one small corollary, so it is probably not worth creating a new name just for it and splitting the introduction of the name from the statement I'm making.