# Suggestion for choosing (building) optimization function

I would like to build a supervised learning model M satisfying the following conditions:

1. Training data $$\{X, Y\}$$, where $$x \in R^m$$ and $$y \in R^n$$

2. Assume: $$M(x) = p$$, then: $$0 < p[k] <= y[k]$$, for all $$k = 1,\dots, n$$. Here I mean $$p[k]$$ as close as possible to $$y[k]$$

Could you please suggest what are the "best" cost function and optimization method that I can use to train this model $$M$$?

Thank you.