Benders decomposition for variational inequalities
A variational inequality problem of the following type is considered: find \((x^*,y^*)\in S=\{(x,y)\); \(A_ 1x+A_ 2y=b\), \(x\in X\), \(y\in Y\}\) such that \(<C_ 1(x^*),x-x^*>+<C_ 2(y^*),y-y^*>\geq 0\) for every (x,y)\(\in S\). Here X and Y are subsets of finite-dimensional spaces, \(A_ 1\) and \(A_ 2\) are linear mappings, \(C_ 1\) and \(C_ 2\) are continuous mappings and \(<,>\) is the scalar product. The authors generalize the decomposition technique of Benders to the above problem with linear constraints. The approach is applied for the decomposition of the traffic assignment problem and is illustrated by a computational example.
scientific article; zbMATH DE number 4191375
scientific article