## Pareto Optimization

This document describes the generalization of the well-known derivative rule for finding the extrema of a function to the case where we have multiple (usually conflicting) objective functions.

### Notation and conventions

We assume that a dependent quantity y can be expressed in terms of a linear function of a number of independent quantities x, i.e.
y = ∑_{j} α_{j}x_{j}.
Note that this expression does not allow for a constant term.
However, this is not a loss of generality: it can be emulated by making
one of the independent quantities, say x_{0}, equal to 1 for all points
in your dataset.

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