Enlargement of Monotone Operators with Applications to Variational Inequalities

摘要: Given a point-to-set operator T, we introduce the Te defined as Te(x)= {u: 〈 u − v, x y 〉 ≥ −e for all ɛ Rn, v T(y)}. When T is maximal monotone inherits most properties of e-subdifferential, e.g. it bounded on sets, Te(x) contains image through sufficiently small ball around x, etc. We prove these and other relevant Te, apply to generate an inexact proximal point method with generalized distances variational inequalities, whose subproblems consist solving problems form 0 He(x), while exact are H(x). If ek coefficient used in kth iteration ek's summable, then sequence generated by algorithm still convergent solution original problem. well behaved enough, set each subproblem solution, so can be finitely solved.