https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12983 Wed 11 Apr 2018 13:43:16 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11701 n : X → Y with g_n(0) = 0 that are Lipschitz continuous in a neighborhood of the origin. Then pick an initial guess x₀ and find a sequence x_n by applying the iteration g_n(x_n1^-x_n)+T(x_n+1) ∋ 0 for n = 0,1,... We prove that if the Lipschitz constants of g_n are bounded by half the reciprocal of the modulus of regularity of T, then there exists a neighborhood O of x̅ (x̅ being a solution to T(x) ∋ 0) such that for each initial point x₀ ∈ O one can find a sequence x_n generated by the algorithm which is linearly convergent to x̅. Moreover, if the functions g_n have their Lipschitz constants convergent to zero, then there exists a sequence starting from x₀ ∈ O which is superlinearly convergent to x̅. Similar convergence results are obtained for the cases when the mapping T is strongly subregular and strongly regular.]]> Sat 24 Mar 2018 10:32:00 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:256 Sat 24 Mar 2018 07:42:56 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27998 gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion and will demonstrate how naturally this gap function arises from the Fitzpatrick function, which is a convex function, used to represent maximal monotone operators. This allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. We also study the special cases of a variational inequality and of a generalized variational inequality problem. The associated notion of a scalar gap is also considered in some detail. Corresponding local and global error bounds are also developed for the maximal monotone inclusion.]]> Sat 24 Mar 2018 07:38:40 AEDT ]]>