In regularization theory, we frequently minimize expressions with the following form: $$x + \lambda y,\ \ \lambda \in \mathbb{R}^+$$ where $x, y$ represent some type of functional and $\lambda \in \mathbb{R}^+$ is a hyperparameter which controls the weighting of the two functionals. I'm interested in ways to restrict the range of $\lambda$ to be finite, e.g. $[0,1]$. For one hyperparameter, this can be easily done as $$\lambda x + (1-\lambda) y, \ \ \lambda \in [0,1].$$
However, for two or more hyperparameters, this quickly becomes quite hairy. One potential expression is $$ \lambda_1 x + (1-\lambda_1)\lambda_2 y + (1-\lambda_1)(1-\lambda_2) z. $$
Is there a way to generalize this range-restriction process for arbitrary number of terms? I was trying to think recursively or through the use of some transformation, but I'm stuck. Any ideas? Thanks in advance.