# Reductions¶

A Reduction is a transformation from one problem to an equivalent problem. Two problems are equivalent if a solution of one can be converted to a solution of the other with no more than a moderate amount of effort. CVXPY uses reductions to rewrite problems into forms that solvers will accept.

Reductions allow CVXPY to simplify problems and target different categories of solvers (quadratic program solvers and conic solvers are two examples of solver categories). Appropriating terminology from software compilers, we classify reductions as either middle-end reductions or back-end reductions. A reduction that simplifies a source problem without regard to the targeted solver is called a middle-end reduction, whereas a reduction that takes a source problem and converts it to a form acceptable to a category of solvers is called a back-end reduction. Each solver (along with the mode in which it is invoked) is called a back-end or target.

The majority of users will not need to know anything about the reduction API; indeed, most users need not even know that reductions exist. But those who wish to extend CVXPY or contribute to it may find the API useful, as might those who are simply curious to learn how CVXPY works.