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Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.
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Accepted
How do you call a linear programming problem when the solution should be "constrained" to a ...
If you are willing to replace $a_i > 0$ by $a_i \ge 0$,
then this becomes a quadratic program. Indeed,
it can be formulated as
\begin{align*}
\text{Minimize}\quad & \frac12 a^\top Q a + q^\top a, \\
…