http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11701 In this paper we consider the following general version of the proximal point algorithm for solving the inclusion T(x) ∋ 0, where T is a set-valued mapping acting from a Banach space X to a Banach space Y. First, choose any sequence of functions g_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. 2012-10-12T02:23:32.391Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:256 In this paper, fundamental mathematical concepts for modeling the dissipative behavior of geomaterials are recalled. These concepts are illustrated on two basic models and applied to derive a new form of the evolution law of the modified Cam-clay model. The aim is to discuss the mathematical structure of the constitutive relationships and its consequences on the structural level. It is recalled that non-differentiable potentials provide an appropriate means of modeling rate-independent behavior. The Cam-clay model is revisited and a standard version is presented. It is seen that this standard version is non-dissipative, which at the same time explains why a non-standard version is needed. The partial normality is exploited and an implicit variational formulation of the modified Cam-clay model is derived. As a result, the solution of boundary-value problems can be replaced by seeking stationary points of a functional. 2010-04-27T05:57:18.685Z ]]>