I want to understand the meaning of the following:

minimize "t" s.t.
E[min (t, sigma y)]> sigma (q/p)
y is geometrically distributed

For simulation purposes it is then said:
Sigma (i1) {i1=1 to infinity} [min (t,i1)* Pr(y=i1)] > q1/p1

I am confused about the interpretation of the above term. Please advice.