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Combinatorics (combinatorial analysis) is a branch of mathematics that studies the discrete objects, the set (a combination, permutation, deployment and transfer of elements) and the relationship to them (eg, partial order).
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Sum of Inverse of Variables in an Optimization Problem
For the discrete version, it can be cast as a mixed-integer linear program. You just have to note that every element $x_i$ can be written as $x_i = \sum_{j=1}^k \frac{\delta_{ij}}{j}$ where $\sum_{j=1 …