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I have a problem which can be written in two ways. A simple example:

More variables, less constraints:

$ min\ x\\ s.t.\ x = \sum_{i} b_iy_i\\ m_1 \leq x \leq M_1\\ m_2 \leq y_i \leq M_2 $

Less variables, more constraints:

$ min\ \sum_{i} b_iy_i\\ s.t.\ m_1 \leq \sum_{i} b_iy_i \leq M_1\\ m_2 \leq y_i \leq M_2 $

The second model only replaces $x$, the result is obviously the same. My question is, will this tradeoff between constraints and variables affect performance of solvers? Will one of these problems be solved faster than the other?

devil0150
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  • For sparse solvers the number of nonzero elements in the coefficient matrix is often more important than the number of variables and equations. Larger and sparser is often better than smaller and denser. But as always: better try it out by timing things. – Erwin Kalvelagen Dec 08 '16 at 22:26

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