  We propose a prototypical Split Inverse Problem (SIP) and a new variational
problem, called the Split Variational Inequality Problem (SVIP), which is a
SIP. It entails finding a solution of one inverse problem (e.g., a Variational
Inequality Problem (VIP)), the image of which under a given bounded linear
transformation is a solution of another inverse problem such as a VIP. We
construct iterative algorithms that solve such problems, under reasonable
conditions, in Hilbert space and then discuss special cases, some of which are
new even in Euclidean space.
