Minimize sum of product of series, given constraints
Given a series $x_t$ and constants $c_1$, $c_2$, I want to find another series $y_t$ such that $\sum_t x_t \cdot y_t$ is minimized, and
$\begin{cases} 0 < \sum_s y_s < c_1 \text{ for all } s \in 0..t\\ -c_2 < y_t < c_2 \end{cases}$
What kind of mathematics do I need to solve this?
Solution 1:
If you change your strict inequalities to weak inequalities, this is a linear programming problem.