Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider an affine variational inequality posed over a polyhedral convex set in n-dimensional Euclidean space. It is often the case that this underlying set has dimension less than n, or has a nontrivial lineality space, or both.  show that when the variational inequality satisfies a ll known regularity condition,  can reduce the problem to the solution of an affine variational inequality in a space of smaller dimension, follod by some simple linear-algebraic calculations. The smaller problem inherits the regularity condition from the original one, and therefore it has a unique solution. The dimension of the space in which the smaller problem is posed equals the rank of the original set: that is, its dimension less the dimension of the lineality space.
['Stephen M. Robinson']
I am writing a research paper on a idea Reduction of affine variational inequalities
[{"from": "human", "value": "I am writing a research paper on a idea Reduction of affine variational inequalities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider an affine variational inequality posed over a polyhedral convex set in n-dimensional Euclidean space. It is often the case that this underlying set has dimension less than n, or has a nontrivial lineality space, or both.  show that when the variational inequality satisfies a ll known regularity condition,  can reduce the problem to the solution of an affine variational inequality in a space of smaller dimension, follod by some simple linear-algebraic calculations. The smaller problem inherits the regularity condition from the original one, and therefore it has a unique solution. The dimension of the space in which the smaller problem is posed equals the rank of the original set: that is, its dimension less the dimension of the lineality space."}]