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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?

Pibben
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jan 03 '22 at 14:12

1 Answers1

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If you change your strict inequalities to weak inequalities, this is a linear programming problem.

RobPratt
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