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In applied mathematics and computer science, variable splitting is a decomposition method that relaxes a set of constraints. ==Details== When the variable ''x'' appears in two sets of constraints, it is possible to substitute the new variables ''x''1 in the first constraints and ''x''2 in the second, and then join the two variables with a new "''linking''" constraint, which requires that : ''x''1=''x''2. 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 ''x''1 and ''x''2 in the new constraint. For many problems, when the equality of the split variables is relaxed, then the system is decomposed, and each subsystem can be solved independently, at substantial reduction of computing time and memory storage. A solution to the relaxed problem (with variable splitting) provides an approximate solution to the original problem: further, the approximate solution to the relaxed problem provides a "warm start", a good initialization of an iterative method for solving the original problem (having only the ''x'' variable).〔〔 Reprinted as Appendix A, in Mikael Adlers, 2000, ''Topics in Sparse Least Squares Problems'', Linkoping Studies in Science and Technology", Linkoping University, Sweden.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Variable splitting」の詳細全文を読む スポンサード リンク
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