Global s-type error bound for the extended linear complementarity problem and applications

Abstract

For the extended linear complementarity problem over an affine subspace, we first study some characterizations of (strong) column/row monotonicity and (strong) R 0-property. We then establish global s-type error bound for this problem with the column monotonicity or R 0-property, especially for the one with the nondegeneracy and column monotonicity, and give several equivalent formulations of such error bound without the square root term for monotone affine variational inequality. Finally, we use this error bound to derive some properties of the iterative sequence produced by smoothing methods for solving such a problem under suitable assumptions.