Algorithms for the Split Variational Inequality Problem

作者：Censor, Yair^*; Gibali, Aviv; Reich, Simeon

来源：Numerical Algorithms, 2012, 59(2): 301-323.

DOI：10.1007/s11075-011-9490-5

• Constrained variational inequality problem
• Hilbert space
• Inverse strongly monotone operator
• Iterative method
• Metric projection
• Monotone operator
• Product space
• Split inverse problem
• Split variational inequality problem
• Variational inequality problem

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.

• 出版日期2012-2