Need help with Minimize

Questions
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1

Hi everyone and thanks in advance for your help.
I used a list of variables to Minimize a particular quantity

Flatten[{ Table[Subscript[P, i], {i, 1, m, 1}], Round[Q], val1}]

How can I define that

 Table[Subscript[P, i], {i, 1, m, 1}]

should be integers??
Any quick idea?

2

Standard procedure (after years everybody should know it by heart): Read in the manual, e.g. about Assumptions, on this page see below $Assumptions and Assuming.