Variable splitting

In applied mathematics and computer science, variable splitting is a decomposition method that relaxes a set of constraints.

in the second, and then join the two variables with a new "linking" constraint,[2] which requires that This new linking constraint can be relaxed with a Lagrange multiplier; in many applications, a Lagrange multiplier can be interpreted as the price of equality between

For many problems, relaxing the equality of split variables allows the system to be broken down, enabling each subsystem to be solved separately.

This significantly reduces computation time and memory usage.

Using an approximate solution as a “warm start” facilitates the iterative solving of the original problem with only the variable

[3] At the same time, M. Guignard and S. Kim introduced the same idea under the name "Lagrangean Decomposition" (their papers appeared in 1987).