The dual gap function for variational inequalities
The dual gap function \(G\) of a variational inequality problem (VIP) was introduced by Marcotte and Zhu. By using some characterizations of \(G\), they studied the relationship among a global error bound, weak sharpness of the solution set, minimum principle sufficiency (MPS) property and finite termination of descent algorithms for the solution of a VIP. Most of their main results require the assumption that the function \(F\) which defines the VIP is pseudo-monotone\(^+\) and the set \(X\) on which the VIP is defined is compact. However, these two conditions are rather strong, reducing too much the class of considered problems. By giving some new characterization of the directional derivative and subdifferential properties of the dual gap function, the authors relax these conditions. As a result one gets a better understanding of the notions of global error bound, weak sharpness of the solution set and MPS property for a VIP.
scientific article; zbMATH DE number 2018229